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# RD Sharma solutions for Class 8 Mathematics chapter 6 - Algebraic Expressions and Identities

## Chapter 6: Algebraic Expressions and Identities

Ex. 6.10Ex. 6.20Ex. 6.30Ex. 6.40Ex. 6.50Ex. 6.60Ex. 6.70

#### Chapter 6: Algebraic Expressions and Identities Exercise 6.10 solutions [Page 2]

Ex. 6.10 | Q 1.1 | Page 2

Identify the term, their coefficients for the following expression:

7x2yz − 5xy

Ex. 6.10 | Q 1.2 | Page 2

Identify the term, their coefficients for the following expression:

x2 + x + 1

Ex. 6.10 | Q 1.3 | Page 2

Identify the term, their coefficients for the following expression:

3x2y2 − 5x2y2z2 + z2

Ex. 6.10 | Q 1.4 | Page 2

Identify the term, their coefficients for the following expression:

9 − ab + bc − ca

Ex. 6.10 | Q 1.5 | Page 2

Identify the term, their coefficients for the following expression:

$\frac{a}{2} + \frac{b}{2} - ab$

Ex. 6.10 | Q 1.6 | Page 2

Identify the term, their coefficients for the following expression:

0.2x − 0.3xy + 0.5y

Ex. 6.10 | Q 2.01 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

x + y

Ex. 6.10 | Q 2.02 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

1000

Ex. 6.10 | Q 2.03 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

x + x2 + x3 + 4y4

Ex. 6.10 | Q 2.04 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

7 + a + 5b

Ex. 6.10 | Q 2.05 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

2b − 3b2

Ex. 6.10 | Q 2.06 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

2y − 3y2 + 4y3

Ex. 6.10 | Q 2.07 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

5x − 4y + 3x

Ex. 6.10 | Q 2.08 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

4a − 15a2

Ex. 6.10 | Q 2.09 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

xy + yz + zt + tx

Ex. 6.10 | Q 2.1 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

pqr

Ex. 6.10 | Q 2.11 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

p2q + pq2

Ex. 6.10 | Q 2.12 | Page 2

Classify the following polynomial as monomial, binomial, trinomial. Which polynomial do not fit in any category?

2p + 2q

#### Chapter 6: Algebraic Expressions and Identities Exercise 6.20 solutions [Pages 5 - 6]

Ex. 6.20 | Q 1.1 | Page 5

3a2b, − 4a2b, 9a2b

Ex. 6.20 | Q 1.2 | Page 5

$\frac{2}{3}a, \frac{3}{5}a, - \frac{6}{5}a$

Ex. 6.20 | Q 1.3 | Page 5

4xy2 − 7x2y, 12x2y − 6xy2, − 3x2y +5xy2

Ex. 6.20 | Q 1.4 | Page 5

$\frac{3}{2}a - \frac{5}{4}b + \frac{2}{5}c, \frac{2}{3}a - \frac{7}{2}b + \frac{7}{2}c, \frac{5}{3}a + \frac{5}{2}b - \frac{5}{4}c$

Ex. 6.20 | Q 1.5 | Page 5

$\frac{11}{2}xy + \frac{12}{5}y + \frac{13}{7}x, - \frac{11}{2}y - \frac{12}{5}x - \frac{13}{7}xy$

Ex. 6.20 | Q 1.6 | Page 5

Add the following algebraic expression: $\frac{7}{2} x^3 - \frac{1}{2} x^2 + \frac{5}{3}, \frac{3}{2} x^3 + \frac{7}{4} x^2 - x + \frac{1}{3}, \frac{3}{2} x^2 - \frac{5}{2}x - 2$

Ex. 6.20 | Q 2.1 | Page 5

Subtract:

− 5xy from 12xy

Ex. 6.20 | Q 2.2 | Page 5

Subtract:

2a2 from − 7a2

Ex. 6.20 | Q 2.3 | Page 5

Subtract:

2a − b from 3a − 5b

Ex. 6.20 | Q 2.4 | Page 5

Subtract:

2x3 − 4x2 + 3x + 5 from 4x3 + x2 + x + 6

Ex. 6.20 | Q 2.5 | Page 5

Subtract:

$\frac{2}{3} y^3 - \frac{2}{7} y^2 - 5 \text { from }\frac{1}{3} y^3 + \frac{5}{7} y^2 + y - 2$

Ex. 6.20 | Q 2.6 | Page 5

Subtract:

$\frac{3}{2}x - \frac{5}{4}y - \frac{7}{2}z \text { from }\frac{2}{3}x + \frac{3}{2}y - \frac{4}{3}z$

Ex. 6.20 | Q 2.7 | Page 5

Subtract:

$x^2 y - \frac{4}{5}x y^2 + \frac{4}{3}xy \text { from } \frac{2}{3} x^2 y + \frac{3}{2}x y^2 - \frac{1}{3}xy$

Ex. 6.20 | Q 2.8 | Page 5

Subtract:

$\frac{ab}{7} - \frac{35}{3}bc + \frac{6}{5}ac \text { from } \frac{3}{5}bc - \frac{4}{5}ac$

Ex. 6.20 | Q 3.1 | Page 5

Take away:

$\frac{6}{5} x^2 - \frac{4}{5} x^3 + \frac{5}{6} + \frac{3}{2}x \text { from }\frac{x^3}{3} - \frac{5}{2} x^2 + \frac{3}{5}x + \frac{1}{4}$

Ex. 6.20 | Q 3.2 | Page 5

Take away:

$\frac{5 a^2}{2} + \frac{3 a^3}{2} + \frac{a}{3} - \frac{6}{5} \text { from } \frac{1}{3} a^3 - \frac{3}{4} a^2 - \frac{5}{2}$

Ex. 6.20 | Q 3.3 | Page 5

Take away:

$\frac{7}{4} x^3 + \frac{3}{5} x^2 + \frac{1}{2}x + \frac{9}{2}\text { from } \frac{7}{2} - \frac{x}{3} - \frac{x^2}{5}$

Ex. 6.20 | Q 3.4 | Page 5

Take away:

$\frac{y^3}{3} + \frac{7}{3} y^2 + \frac{1}{2}y + \frac{1}{2} \text { from } \frac{1}{3} - \frac{5}{3} y^2$

Ex. 6.20 | Q 3.5 | Page 5

Take away:

$\frac{2}{3}ac - \frac{5}{7}ab + \frac{2}{3}bc\text { from } \frac{3}{2}ab - \frac{7}{4}ac - \frac{5}{6}bc$

Ex. 6.20 | Q 4 | Page 6

Subtract 3x − 4y − 7z from the sum of x − 3y + 2z and − 4x + 9y − 11z.

Ex. 6.20 | Q 5 | Page 6

Subtract the sum of 3l − 4m − 7n2 and 2l + 3m − 4n2 from the sum of 9l + 2m − 3n2 and − 3l + m + 4n2 .....

Ex. 6.20 | Q 6 | Page 6

Subtract the sum of 2x − x2 + 5 and − 4x − 3 + 7x2 from 5.

Ex. 6.20 | Q 7.1 | Page 6

Simplify the following:

x2 − 3x + 5 −  $\frac{1}{2}$ (3x2 − 5x + 7)

Ex. 6.20 | Q 7.2 | Page 6

Simplify the following:

[5 − 3x + 2y − (2x − y)] − (3x − 7y + 9)

Ex. 6.20 | Q 7.3 | Page 6

Simplify the following:

$\frac{11}{2} x^2 y - \frac{9}{4}x y^2 + \frac{1}{4}xy - \frac{1}{14} y^2 x + \frac{1}{15}y x^2 + \frac{1}{2}xy$

Ex. 6.20 | Q 7.4 | Page 6

Simplify the following:

$\left( \frac{1}{3} y^2 - \frac{4}{7}y + 11 \right) - \left( \frac{1}{7}y - 3 + 2 y^2 \right) - \left( \frac{2}{7}y - \frac{2}{3} y^2 + 2 \right)$

Ex. 6.20 | Q 7.5 | Page 6

Simplify the following: $- \frac{1}{2} a^2 b^2 c + \frac{1}{3}a b^2 c - \frac{1}{4}ab c^2 - \frac{1}{5}c b^2 a^2 + \frac{1}{6}c b^2 a - \frac{1}{7} c^2 ab + \frac{1}{8}c a^2 b .$

#### Chapter 6: Algebraic Expressions and Identities Exercise 6.30 solutions [Pages 13 - 14]

Ex. 6.30 | Q 1 | Page 13

Find each of the following product:
5x2 × 4x3

Ex. 6.30 | Q 2 | Page 13

Find each of the following product:
−3a2 × 4b4

Ex. 6.30 | Q 3 | Page 13

Find each of the following product:
(−5xy) × (−3x2yz)

Ex. 6.30 | Q 4 | Page 13

Find each of the following product:

$\frac{1}{4}xy \times \frac{2}{3} x^2 y z^2$

Ex. 6.30 | Q 5 | Page 14

Find each of the following product:

$\left( - \frac{7}{5}x y^2 z \right) \times \left( \frac{13}{3} x^2 y z^2 \right)$

Ex. 6.30 | Q 6 | Page 14

Find each of the following product: $\left( \frac{- 24}{25} x^3 z \right) \times \left( - \frac{15}{16}x z^2 y \right)$

Ex. 6.30 | Q 7 | Page 14

Find each of the following product:

$\left( - \frac{1}{27} a^2 b^2 \right) \times \left( \frac{9}{2} a^3 b^2 c^2 \right)$

Ex. 6.30 | Q 8 | Page 14

Find each of the following product: $( - 7xy) \times \left( \frac{1}{4} x^2 yz \right)$

Ex. 6.30 | Q 9 | Page 14

Find each of the following product:
(7ab) × (−5ab2c) × (6abc2)

Ex. 6.30 | Q 10 | Page 14

Find each of the following product:
(−5a) × (−10a2) × (−2a3)

Ex. 6.30 | Q 11 | Page 14

Find each of the following product:
(−4x2) × (−6xy2) × (−3yz2)

Ex. 6.30 | Q 12 | Page 14

Find each of the following product:

$\left( - \frac{2}{7} a^4 \right) \times \left( - \frac{3}{4} a^2 b \right) \times \left( - \frac{14}{5} b^2 \right)$

Ex. 6.30 | Q 13 | Page 14

Find each of the following product: $\left( \frac{7}{9}a b^2 \right) \times \left( \frac{15}{7}a c^2 b \right) \times \left( - \frac{3}{5} a^2 c \right)$

Ex. 6.30 | Q 14 | Page 14

Find each of the following product: $\left( \frac{4}{3} u^2 vw \right) \times \left( - 5uv w^2 \right) \times \left( \frac{1}{3} v^2 wu \right)$

Ex. 6.30 | Q 15 | Page 14

Find each of the following product:

$\left( 0 . 5x \right) \times \left( \frac{1}{3}x y^2 z^4 \right) \times \left( 24 x^2 yz \right)$

Ex. 6.30 | Q 16 | Page 14

Find each of the following product: $\left( \frac{4}{3}p q^2 \right) \times \left( - \frac{1}{4} p^2 r \right) \times \left( 16 p^2 q^2 r^2 \right)$

Ex. 6.30 | Q 17 | Page 14

Find each of the following product:
(2.3xy) × (0.1x) × (0.16)

Ex. 6.30 | Q 18 | Page 14

Express each of the following product as a monomials and verify the result in each case for x = 1:
(3x) × (4x) × (−5x)

Ex. 6.30 | Q 19 | Page 14

Express each of the following product as a monomials and verify the result in each case for x = 1:
(4x2) × (−3x) × $\left( \frac{4}{5} x^3 \right)$

Ex. 6.30 | Q 20 | Page 14

Express each of the following product as a monomials and verify the result in each case for x = 1:
(5x4) × (x2)3 × (2x)2

Ex. 6.30 | Q 21 | Page 14

Express each of the following product as a monomials and verify the result in each case for x = 1:
(x2)3 × (2x) × (−4x) × (5)

Ex. 6.30 | Q 22 | Page 14

Write down the product of −8x2y6 and −20xy. Verify the product for x = 2.5, y = 1.

Ex. 6.30 | Q 23 | Page 14

Evaluate (3.2x6y3) × (2.1x2y2) when x = 1 and y = 0.5.

Ex. 6.30 | Q 24 | Page 14

Find the value of (5x6) × (−1.5x2y3) × (−12xy2) when x = 1, y = 0.5.

Ex. 6.30 | Q 25 | Page 14

Evaluate (2.3a5b2) × (1.2a2b2) when a = 1 and b = 0.5.

Ex. 6.30 | Q 26 | Page 14

Evaluate (−8x2y6) × (−20xy) for x = 2.5 and y = 1.

Ex. 6.30 | Q 27 | Page 14

Express each of the following product as a monomials and verify the result for x = 1, y = 2:
(−xy3) × (yx3) × (xy)

Ex. 6.30 | Q 28 | Page 14

Express each of the following product as a monomials and verify the result for x = 1, y = 2: $\left( \frac{1}{8} x^2 y^4 \right) \times \left( \frac{1}{4} x^4 y^2 \right) \times \left( xy \right) \times 5$

Ex. 6.30 | Q 29 | Page 14

Express each of the following product as a monomials and verify the result for x = 1, y = 2:

$\left( \frac{2}{5} a^2 b \right) \times \left( - 15 b^2 ac \right) \times \left( - \frac{1}{2} c^2 \right)$
Ex. 6.30 | Q 30 | Page 14

Express each of the following product as a monomials and verify the result for x = 1, y = 2: $\left( - \frac{4}{7} a^2 b \right) \times \left( - \frac{2}{3} b^2 c \right) \times \left( - \frac{7}{6} c^2 a \right)$

Ex. 6.30 | Q 31 | Page 14

Express each of the following product as a monomials and verify the result for x = 1, y = 2:

$\left( \frac{4}{9}ab c^3 \right) \times \left( - \frac{27}{5} a^3 b^2 \right) \times \left( - 8 b^3 c \right)$

Ex. 6.30 | Q 32 | Page 14

Evaluate each of the following when x = 2, y = −1.

$(2xy) \times \left( \frac{x^2 y}{4} \right) \times \left( x^2 \right) \times \left( y^2 \right)$

Ex. 6.30 | Q 33 | Page 14

Evaluate each of the following when x = 2, y = −1.

$\left( \frac{3}{5} x^2 y \right) \times \left( - \frac{15}{4}x y^2 \right) \times \left( \frac{7}{9} x^2 y^2 \right)$

#### Chapter 6: Algebraic Expressions and Identities Exercise 6.40 solutions [Page 21]

Ex. 6.40 | Q 1 | Page 21

Find the following product:
2a3(3a + 5b)

Ex. 6.40 | Q 2 | Page 21

Find the following product:
−11a(3a + 2b)

Ex. 6.40 | Q 3 | Page 21

Find the following product:
−5a(7a − 2b)

Ex. 6.40 | Q 4 | Page 21

Find the following product:
−11y2(3y + 7)

Ex. 6.40 | Q 5 | Page 21

Find the following product: $\frac{6x}{5}( x^3 + y^3 )$

Ex. 6.40 | Q 6 | Page 21

xy(x3 − y3)

Ex. 6.40 | Q 7 | Page 21

Find the following product:
0.1y(0.1x5 + 0.1y)

Ex. 6.40 | Q 8 | Page 21

Find the following product: $\left( - \frac{7}{4}a b^2 c - \frac{6}{25} a^2 c^2 \right)( - 50 a^2 b^2 c^2 )$

Ex. 6.40 | Q 9 | Page 21

Find the following product: $- \frac{8}{27}xyz\left( \frac{3}{2}xy z^2 - \frac{9}{4}x y^2 z^3 \right)$

Ex. 6.40 | Q 10 | Page 21

Find the following product: $- \frac{4}{27}xyz\left( \frac{9}{2} x^2 yz - \frac{3}{4}xy z^2 \right)$

Ex. 6.40 | Q 11 | Page 21

Find the following product:
1.5x(10x2y − 100xy2)

Ex. 6.40 | Q 12 | Page 21

Find the following product:
4.1xy(1.1x − y)

Ex. 6.40 | Q 13 | Page 21

Find the following product:
250.5xy $\left( xz + \frac{y}{10} \right)$

Ex. 6.40 | Q 14 | Page 21

Find the following product: $\frac{7}{5} x^2 y\left( \frac{3}{5}x y^2 + \frac{2}{5}x \right)$

Ex. 6.40 | Q 15 | Page 21

Find the following product: $\frac{4}{3}a( a^2 + b^2 - 3 c^2 )$

Ex. 6.40 | Q 16 | Page 21

Find the product 24x2 (1 − 2x) and evaluate its value for x = 3.

Ex. 6.40 | Q 17 | Page 21

Find the product −3y(xy + y2) and find its value for x = 4 and y = 5.

Ex. 6.40 | Q 18 | Page 21

Multiply $- \frac{3}{2} x^2 y^3 by (2x - y)$ and verify the answer for x = 1 and y = 2.

Ex. 6.40 | Q 19.1 | Page 21

Multiply the monomial by the binomial and find the value for x = −1, y = 0.25 and z = 0.05: 15y2(2 − 3x)

Ex. 6.40 | Q 19.2 | Page 21

Multiply the monomial by the binomial and find the value for x = −1, y = 0.25 and z = 0.05: −3x(y2 + z2)

Ex. 6.40 | Q 19.3 | Page 21

Multiply the monomial by the binomial and find the value for x = −1, y = 0.25 and z = 0.05: z2(x − y)

Ex. 6.40 | Q 19.4 | Page 21

Multiply the monomial by the binomial and find the value for x = −1, y = 0.25 and z = 0.05:

xz(x2 + y2)

Ex. 6.40 | Q 20.01 | Page 21

Simplify: 2x2(x3 − x) − 3x(x4 + 2x) − 2(x4 − 3x2)

Ex. 6.40 | Q 20.02 | Page 21

Simplify: x3y(x2 − 2x) + 2xy(x3 − x4)

Ex. 6.40 | Q 20.03 | Page 21

Simplify: 3a2 + 2(a + 2) − 3a(2a + 1)

Ex. 6.40 | Q 20.04 | Page 21

Simplify: x(x + 4) + 3x(2x2 − 1) + 4x2 + 4

Ex. 6.40 | Q 20.05 | Page 21

Simplify:  a(b − c) − b(c − a) − c(a − b)

Ex. 6.40 | Q 20.06 | Page 21

Simplify: a(b − c) + b(c − a) + c(a − b)

Ex. 6.40 | Q 20.07 | Page 21

Simplify: 4ab(a − b) − 6a2(b − b2) − 3b2(2a2 − a) + 2ab(b − a)

Ex. 6.40 | Q 20.08 | Page 21

Simplify:  x2(x2 + 1) − x3(x + 1) − x(x3 − x)

Ex. 6.40 | Q 20.09 | Page 21

Simplify:   2a2 + 3a(1 − 2a3) + a(a + 1)

Ex. 6.40 | Q 20.1 | Page 21

Simplify: a2(2a − 1) + 3a + a3 − 8

Ex. 6.40 | Q 20.11 | Page 21

Simplify: $\frac{3}{2} x^2 ( x^2 - 1) + \frac{1}{4} x^2 ( x^2 + x) - \frac{3}{4}x( x^3 - 1)$

Ex. 6.40 | Q 20.12 | Page 21

Simplify: a2b(a − b2) + ab2(4ab − 2a2) − a3b(1 − 2b)

Ex. 6.40 | Q 20.13 | Page 21

Simplify:  a2b(a3 − a + 1) − ab(a4 − 2a2 + 2a) − b (a3 − a2 − 1)

#### Chapter 6: Algebraic Expressions and Identities Exercise 6.50 solutions [Pages 30 - 31]

Ex. 6.50 | Q 1 | Page 30

Multiply:
(5x + 3) by (7x + 2)

Ex. 6.50 | Q 2 | Page 30

Multiply:
(2x + 8) by (x − 3)

Ex. 6.50 | Q 3 | Page 30

Multiply:
(7x + y) by (x + 5y)

Ex. 6.50 | Q 4 | Page 30

Multiply:
(a − 1) by (0.1a2 + 3)

Ex. 6.50 | Q 5 | Page 30

Multiply:
(3x2 + y2) by (2x2 + 3y2)

Ex. 6.50 | Q 6 | Page 30

Multiply: $\left( \frac{3}{5}x + \frac{1}{2}y \right) by \left( \frac{5}{6}x + 4y \right)$

Ex. 6.50 | Q 7 | Page 31

Multiply:
(x6 − y6) by (x2 + y2)

Ex. 6.50 | Q 8 | Page 31

Multiply:
(x2 + y2) by (3a + 2b)

Ex. 6.50 | Q 9 | Page 31

Multiply:
[−3d + (−7f)] by (5d + f)

Ex. 6.50 | Q 10 | Page 31

Multiply:
(0.8a − 0.5b) by (1.5a − 3b)

Ex. 6.50 | Q 11 | Page 31

Multiply:
(2x2y2 − 5xy2) by (x2 − y2)

Ex. 6.50 | Q 12 | Page 31

Multiply: $\left( \frac{x}{7} + \frac{x^2}{2} \right)by\left( \frac{2}{5} + \frac{9x}{4} \right)$

Ex. 6.50 | Q 13 | Page 31

Multiply: $\left( - \frac{a}{7} + \frac{a^2}{9} \right)by\left( \frac{b}{2} - \frac{b^2}{3} \right)$.

Ex. 6.50 | Q 14 | Page 31

Multiply:
(3x2y − 5xy2) by  $\left( \frac{1}{5} x^2 + \frac{1}{3} y^2 \right)$.

Ex. 6.50 | Q 15 | Page 31

Multiply:
(2x2 − 1) by (4x3 + 5x2)

Ex. 6.50 | Q 16 | Page 31

(2xy + 3y2) (3y2 − 2)

Ex. 6.50 | Q 17 | Page 31

Find the following product and verify the result for x = − 1, y = − 2:
(3x − 5y) (x + y)

Ex. 6.50 | Q 18 | Page 31

Find the following product and verify the result for x = − 1, y = − 2:
(x2y − 1) (3 − 2x2y)

Ex. 6.50 | Q 19 | Page 31

Find the following product and verify the result for x = − 1, y = − 2: $\left( \frac{1}{3}x - \frac{y^2}{5} \right)\left( \frac{1}{3}x + \frac{y^2}{5} \right)$

Ex. 6.50 | Q 20 | Page 31

Simplify:
x2(x + 2y) (x − 3y)

Ex. 6.50 | Q 21 | Page 31

Simplify:
(x2 − 2y2) (x + 4y) x2y2

Ex. 6.50 | Q 22 | Page 31

Simplify:
a2b2(a + 2b)(3a + b)

Ex. 6.50 | Q 23 | Page 31

Simplify:
x2(x − y) y2(x + 2y)

Ex. 6.50 | Q 24 | Page 31

Simplify:
(x3 − 2x2 + 5x − 7)(2x − 3)

Ex. 6.50 | Q 25 | Page 31

Simplify:
(5x + 3)(x − 1)(3x − 2)

Ex. 6.50 | Q 26 | Page 31

Simplify:
(5 − x)(6 − 5x)( 2 − x)

Ex. 6.50 | Q 27 | Page 31

Simplify:
(2x2 + 3x − 5)(3x2 − 5x + 4)

Ex. 6.50 | Q 28 | Page 31

Simplify:
(3x − 2)(2x − 3) + (5x − 3)(x + 1)

Ex. 6.50 | Q 29 | Page 31

Simplify:
(5x − 3)(x + 2) − (2x + 5)(4x − 3)

Ex. 6.50 | Q 30 | Page 31

Simplify:
(3x + 2y)(4x + 3y) − (2x − y)(7x − 3y)

Ex. 6.50 | Q 31 | Page 31

Simplify:
(x2 − 3x + 2)(5x − 2) − (3x2 + 4x − 5)(2x − 1)

Ex. 6.50 | Q 32 | Page 31

Simplify:
(x3 − 2x2 + 3x − 4) (x −1) − (2x − 3)(x2 − x + 1)

#### Chapter 6: Algebraic Expressions and Identities Exercise 6.60 solutions [Pages 43 - 44]

Ex. 6.60 | Q 1.01 | Page 43

Write the following square of binomial as trinomial: (x + 2)2

Ex. 6.60 | Q 1.02 | Page 43

Write the following square of binomial as trinomial:  (8a + 3b)2

Ex. 6.60 | Q 1.03 | Page 43

Write the following square of binomial as trinomial:  (2m + 1)2

Ex. 6.60 | Q 1.04 | Page 43

Write the following square of binomial as trinomial:  $\left( 9a + \frac{1}{6} \right)^2$

Ex. 6.60 | Q 1.05 | Page 43

Write the following square of binomial as trinomial:

$\left( x + \frac{x^2}{2} \right)^2$

Ex. 6.60 | Q 1.06 | Page 43

Write the following square of binomial as trinomial:  $\left( \frac{x}{4} - \frac{y}{3} \right)$

Ex. 6.60 | Q 1.07 | Page 43

Write the following square of binomial as trinomial:  $\left( 3x - \frac{1}{3x} \right)^2$

Ex. 6.60 | Q 1.08 | Page 43

Write the following square of binomial as trinomial:  $\left( \frac{x}{y} - \frac{y}{x} \right)^2$

Ex. 6.60 | Q 1.09 | Page 43

Write the following square of binomial as trinomial: $\left( \frac{3a}{2} - \frac{5b}{4} \right)^2$

Ex. 6.60 | Q 1.1 | Page 43

Write the following square of binomial as trinomial: (a2b − bc2)2

Ex. 6.60 | Q 1.11 | Page 43

Write the following square of binomial as trinomial:  $\left( \frac{2a}{3b} + \frac{2b}{3a} \right)^2$

Ex. 6.60 | Q 1.12 | Page 43

Write the following square of binomial as trinomial:  (x2 − ay)2

Ex. 6.60 | Q 2.1 | Page 43

Find the product of the following binomial: (2x + y)(2x + y)

Ex. 6.60 | Q 2.2 | Page 43

Find the product of the following binomial:  (a + 2b)(a − 2b)

Ex. 6.60 | Q 2.3 | Page 43

Find the product of the following binomial:  (a2 + bc)(a− bc)

Ex. 6.60 | Q 2.4 | Page 43

Find the product of the following binomial: $\left( \frac{4x}{5} - \frac{3y}{4} \right)\left( \frac{4x}{5} + \frac{3y}{4} \right)$

Ex. 6.60 | Q 2.5 | Page 43

Find the product of the following binomial: $\left( 2x + \frac{3}{y} \right)\left( 2x - \frac{3}{y} \right)$

Ex. 6.60 | Q 2.6 | Page 43

Find the product of the following binomial: (2a3 + b3)(2a3 − b3)

Ex. 6.60 | Q 2.7 | Page 43

Find the product of the following binomial: $\left( x^4 + \frac{2}{x^2} \right)\left( x^4 - \frac{2}{x^2} \right)$

Ex. 6.60 | Q 2.8 | Page 43

Find the product of the following binomial: $\left( x^3 + \frac{1}{x^3} \right)\left( x^3 - \frac{1}{x^3} \right)$

Ex. 6.60 | Q 3.1 | Page 43

Using the formula for squaring a binomial, evaluate the following:  (102)2

Ex. 6.60 | Q 3.2 | Page 43

Using the formula for squaring a binomial, evaluate the following: (99)2

Ex. 6.60 | Q 3.3 | Page 43

Using the formula for squaring a binomial, evaluate the following:  (1001)2

Ex. 6.60 | Q 3.4 | Page 43

Using the formula for squaring a binomial, evaluate the following:  (999)2

Ex. 6.60 | Q 3.5 | Page 43

Using the formula for squaring a binomial, evaluate the following:  (703)2

Ex. 6.60 | Q 4.1 | Page 43

Simplify the following using the formula: (a − b)(a + b) = a2 − b2: (82)2 − (18)2

Ex. 6.60 | Q 4.2 | Page 43

Simplify the following using the formula: (a − b)(a + b) = a2 − b2: (467)2 − (33)2

Ex. 6.60 | Q 4.3 | Page 43

Simplify the following using the formula: (a − b)(a + b) = a2 − b2: (79)2 − (69)2

Ex. 6.60 | Q 4.4 | Page 43

Simplify the following using the formula: (a − b)(a + b) = a2 − b2: 197 × 203

Ex. 6.60 | Q 4.5 | Page 43

Simplify the following using the formula: (a − b)(a + b) = a2 − b2: 113 × 87

Ex. 6.60 | Q 4.6 | Page 43

Simplify the following using the formula: (a − b)(a + b) = a2 − b2: 95 × 105

Ex. 6.60 | Q 4.7 | Page 43

Simplify the following using the formula: (a − b)(a + b) = a2 − b2: 1.8 × 2.2

Ex. 6.60 | Q 4.8 | Page 43

Simplify the following using the formula: (a − b)(a + b) = a2 − b2:  9.8 × 10.2

Ex. 6.60 | Q 5.1 | Page 43

Simplify the following using the identities: $\frac{{58}^2 - {42}^2}{16}$

Ex. 6.60 | Q 5.2 | Page 43

Simplify the following using the identities: 178 × 178 − 22 × 22

Ex. 6.60 | Q 5.3 | Page 43

Simplify the following using the identities: $\frac{198 \times 198 - 102 \times 102}{96}$

Ex. 6.60 | Q 5.4 | Page 43

Simplify the following using the identities:  1.73 × 1.73 − 0.27 × 0.27

Ex. 6.60 | Q 5.5 | Page 43

Simplify the following using the identities: $\frac{8 . 63 \times 8 . 63 - 1 . 37 \times 1 . 37}{0 . 726}$

Ex. 6.60 | Q 6.1 | Page 43

Find the value of x, if 4x = (52)2 − (48)2.

Ex. 6.60 | Q 6.2 | Page 43

Find the value of x, if 14x = (47)2 − (33)2.

Ex. 6.60 | Q 6.3 | Page 43

Find the value of x, if 5x = (50)2 − (40)2.

Ex. 6.60 | Q 7 | Page 43

If $x + \frac{1}{x} = 20,$find the value of $x^2 + \frac{1}{x^2} .$.

Ex. 6.60 | Q 8 | Page 43

If $x - \frac{1}{x} = 3,$  find the values of $x^2 + \frac{1}{x^2}$ and $x^4 + \frac{1}{x^4} .$

Ex. 6.60 | Q 9 | Page 43

If $x^2 + \frac{1}{x^2} = 18,$  find the values of $x + \frac{1}{x} \text { and } x - \frac{1}{x} .$

Ex. 6.60 | Q 10 | Page 43

If x + y = 4 and xy = 2, find the value of x2 + y2

Ex. 6.60 | Q 11 | Page 43

If x − y = 7 and xy = 9, find the value of x2 + y2

Ex. 6.60 | Q 12 | Page 44

If 3x + 5y = 11 and xy = 2, find the value of 9x2 + 25y2

Ex. 6.60 | Q 13.1 | Page 44

Find the value of the following expression: 16x2 + 24x + 9, when $x = \frac{7}{4}$

Ex. 6.60 | Q 13.2 | Page 44

Find the value of the following expression:  64x2 + 81y2 + 144xy, when x = 11 and $y = \frac{4}{3}$

Ex. 6.60 | Q 13.3 | Page 44

Find the value of the following expression:  81x2 + 16y2 − 72xy, when $x = \frac{2}{3}$ and  $y = \frac{3}{4}$

Ex. 6.60 | Q 14 | Page 44

If $x + \frac{1}{x} = 9,$  find the value of $x^4 + \frac{1}{x^4} .$

Ex. 6.60 | Q 15 | Page 44

If $x + \frac{1}{x} = 12,$  find the value of $x - \frac{1}{x} .$

Ex. 6.60 | Q 16 | Page 44

If 2x + 3y = 14 and 2x − 3y = 2, find the value of xy.
[Hint: Use (2x + 3y)2 − (2x − 3y)2 = 24xy]

Ex. 6.60 | Q 17.1 | Page 44

If x2 + y2 = 29 and xy = 2, find the value of x + y.

Ex. 6.60 | Q 17.2 | Page 44

If x2 + y2 = 29 and xy = 2, find the value of x - y.

Ex. 6.60 | Q 17.3 | Page 44

If x2 + y2 = 29 and xy = 2, find the value of x4 + y4 .

Ex. 6.60 | Q 18.1 | Page 44

What must be added to the following expression to make it a whole square?

4x2 − 12x + 7

Ex. 6.60 | Q 18.2 | Page 44

What must be added to the following expression to make it a whole square?

4x2 − 20x + 20

Ex. 6.60 | Q 19.1 | Page 44

Simplify : (x − y)(x + y) (x2 + y2)(x4 + y2)

Ex. 6.60 | Q 19.2 | Page 44

Simplify : (2x − 1)(2x + 1)(4x2 + 1)(16x4 + 1)

Ex. 6.60 | Q 19.3 | Page 44

Simplify : (4m − 8n)2 + (7m + 8n)2

Ex. 6.60 | Q 19.4 | Page 44

Simplify : (2.5p − 1.5q)2 − (1.5p − 2.5q)2

Ex. 6.60 | Q 19.5 | Page 44

Simplify :  (m2 − n2m)2 + 2m3n2

Ex. 6.60 | Q 20.1 | Page 44

Show that:  (3x + 7)2 − 84x = (3x − 7)2

Ex. 6.60 | Q 20.2 | Page 44

Show that:  (9a − 5b)2 + 180ab = (9a + 5b)

Ex. 6.60 | Q 20.3 | Page 44

Show that: $\left( \frac{4m}{3} - \frac{3n}{4} \right)^2 + 2mn = \frac{16 m^2}{9} + \frac{9 n^2}{16}$

Ex. 6.60 | Q 20.4 | Page 44

Show that:  (4pq + 3q)2 − (4pq − 3q)2 = 48pq2

Ex. 6.60 | Q 20.5 | Page 44

Show that:  (a − b)(a + b) + (b − c)(b + c) + (c − a)( c + a) = 0

#### Chapter 6: Algebraic Expressions and Identities Exercise 6.70 solutions [Page 47]

Ex. 6.70 | Q 1.01 | Page 47

Find the following product: (x + 4) (x + 7)

Ex. 6.70 | Q 1.02 | Page 47

Find the following product:  (x − 11) (x + 4)

Ex. 6.70 | Q 1.03 | Page 47

Find the following product: (x + 7) (x − 5)

Ex. 6.70 | Q 1.04 | Page 47

Find the following product: (x − 3) ( x − 2)

Ex. 6.70 | Q 1.05 | Page 47

Find the following product: (y2 − 4) (y2 − 3)

Ex. 6.70 | Q 1.06 | Page 47

Find the following product: $\left( x + \frac{4}{3} \right)\left( x + \frac{3}{4} \right)$

Ex. 6.70 | Q 1.07 | Page 47

Find the following product: (3x + 5) (3x + 11)

Ex. 6.70 | Q 1.08 | Page 47

Find the following product:  (2x2 − 3) (2x2 + 5)

Ex. 6.70 | Q 1.09 | Page 47

Find the following product: (z2 + 2) (z2 − 3)

Ex. 6.70 | Q 1.1 | Page 47

Find the following product: (3x − 4y) (2x − 4y)

Ex. 6.70 | Q 1.11 | Page 47

Find the following product:  (3x2 − 4xy) (3x2 − 3xy)

Ex. 6.70 | Q 1.12 | Page 47

Find the following product: $\left( x + \frac{1}{5} \right)(x + 5)$

Ex. 6.70 | Q 1.13 | Page 47

Find the following product: $\left( z + \frac{3}{4} \right)\left( z + \frac{4}{3} \right)$

Ex. 6.70 | Q 1.14 | Page 47

Find the following product:  (x2 + 4) (x2 + 9)

Ex. 6.70 | Q 1.15 | Page 47

Find the following product: (y2 + 12) (y2 + 6)

Ex. 6.70 | Q 1.16 | Page 47

Find the following product: $\left( y^2 + \frac{5}{7} \right)\left( y^2 - \frac{14}{5} \right)$

Ex. 6.70 | Q 1.17 | Page 47

Find the following product:  (p2 + 16) $\left( p^2 - \frac{1}{4} \right)$

Ex. 6.70 | Q 2.1 | Page 47

Evaluate the following: 102 × 106

Ex. 6.70 | Q 2.2 | Page 47

Evaluate the following: 109 × 107

Ex. 6.70 | Q 2.3 | Page 47

Evaluate the following: 35 × 37

Ex. 6.70 | Q 2.4 | Page 47

Evaluate the following: 53 × 55

Ex. 6.70 | Q 2.5 | Page 47

Evaluate the following: 103 × 96

Ex. 6.70 | Q 2.6 | Page 47

Evaluate the following: 34 × 36

Ex. 6.70 | Q 2.7 | Page 47

Evaluate the following: 994 × 1006

## Chapter 6: Algebraic Expressions and Identities

Ex. 6.10Ex. 6.20Ex. 6.30Ex. 6.40Ex. 6.50Ex. 6.60Ex. 6.70

## RD Sharma solutions for Class 8 Mathematics chapter 6 - Algebraic Expressions and Identities

RD Sharma solutions for Class 8 Maths chapter 6 (Algebraic Expressions and Identities) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 8 by R D Sharma (2019-2020 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 8 Mathematics chapter 6 Algebraic Expressions and Identities are Concept of Expression, Terms, Factors and Coefficients, Monomials, Binomials and Polynomials, Like and Unlike Terms, Addition and Subtraction of Algebraic Expressions, Multiplication of Algebraic Expressions: Introduction, Multiplying Two Monomials, Multiplying Three Or More Monomials, Multiplying a Monomial by a Binomial, Multiplying a Monomial by a Trinomial, Multiplying a Binomial by a Binomial, Multiplying a Binomial by a Trinomial, Concept of Identity, Standard Identities, Applying Identities.

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