# Selina solutions for Concise Mathematics Class 8 ICSE chapter 12 - Identities [Latest edition]

## Chapter 12: Identities

Exercise 12 (A)Exercise 12 (B)Exercise 12 (C)Exercise 12 (D)
Exercise 12 (A) [Page 150]

### Selina solutions for Concise Mathematics Class 8 ICSE Chapter 12 Identities Exercise 12 (A) [Page 150]

Exercise 12 (A) | Q 1.1 | Page 150

Use direct method to evaluate the following products :
(x + 8)(x + 3)

Exercise 12 (A) | Q 1.2 | Page 150

Use the direct method to evaluate the following products :
(y + 5)(y – 3)

Exercise 12 (A) | Q 1.3 | Page 150

Use the direct method to evaluate the following products :
(a – 8) (a + 2)

Exercise 12 (A) | Q 1.4 | Page 150

Use the direct method to evaluate the following products :
(b – 3) (b – 5)

Exercise 12 (A) | Q 1.5 | Page 150

Use the direct method to evaluate the following products :
(3x – 2y) (2x + y)

Exercise 12 (A) | Q 1.6 | Page 150

Use the direct method to evaluate the following products :
(5a + 16) (3a – 7)

Exercise 12 (A) | Q 1.7 | Page 150

Use the direct method to evaluate the following products :
(8 – b) (3 + b)

Exercise 12 (A) | Q 2.01 | Page 150

Use the direct method to evaluate :
(x+1) (x−1)

Exercise 12 (A) | Q 2.02 | Page 150

Use the direct method to evaluate :
(2+a) (2−a)

Exercise 12 (A) | Q 2.03 | Page 150

Use the direct method to evaluate :
(3b−1) (3b+1)

Exercise 12 (A) | Q 2.04 | Page 150

Use the direct method to evaluate :
(4+5x) (4−5x)

Exercise 12 (A) | Q 2.05 | Page 150

Use the direct method to evaluate :
(2a+3) (2a−3)

Exercise 12 (A) | Q 2.06 | Page 150

Use the direct method to evaluate :
(xy+4) (xy−4)

Exercise 12 (A) | Q 2.07 | Page 150

Use the direct method to evaluate :
(ab+x2) (ab−x2)

Exercise 12 (A) | Q 2.08 | Page 150

Use the direct method to evaluate :
(3x2+5y2) (3x2−5y2)

Exercise 12 (A) | Q 2.09 | Page 150

Use the direct method to evaluate :
("z"-2/3)("z"+2/3)

Exercise 12 (A) | Q 2.1 | Page 150

Use the direct method to evaluate :
(3/5"a"+1/2)(3/5"a"-1/2)

Exercise 12 (A) | Q 2.11 | Page 150

Use the direct method to evaluate :
(0.5a−2a) (0.5+2a)

Exercise 12 (A) | Q 2.12 | Page 150

Use the direct method to evaluate :
("a"/2-"b"/3)("a"/2+"b"/3)

Exercise 12 (A) | Q 3.1 | Page 150

Evaluate : (a+1) (a-1) (a2+1)

Exercise 12 (A) | Q 3.2 | Page 150

Evaluate : (a+b) (a−b) (a2+b2)

Exercise 12 (A) | Q 3.3 | Page 150

Evaluate : (2a−b) (2a+b) (4a2+b2)

Exercise 12 (A) | Q 3.4 | Page 150

Evaluate : (3−2x) (3+2x) (9+4x2)

Exercise 12 (A) | Q 3.5 | Page 150

Evaluate : (3x−4y) (3x+4y) (9x2+16y2)

Exercise 12 (A) | Q 4.1 | Page 150

Use the product (a + b) (a – b) = a2 – b2 to evaluate:
21 x 19

Exercise 12 (A) | Q 4.2 | Page 150

Use the product (a + b) (a – b) = a2 – b2 to evaluate:
33 x 27

Exercise 12 (A) | Q 4.3 | Page 150

Use the product (a + b) (a – b) = a2 – b2 to evaluate:
103 x 97

Exercise 12 (A) | Q 4.4 | Page 150

Use the product (a + b) (a – b) = a2 – b2 to evaluate:
9.8 x 10.2

Exercise 12 (A) | Q 4.5 | Page 150

Use the product (a + b) (a – b) = a2 – b2 to evaluate:
7.7 x 8.3

Exercise 12 (A) | Q 4.6 | Page 150

Use the product (a + b) (a – b) = a2 – b2 to evaluate:
4.6 x 5.4

Exercise 12 (A) | Q 5.01 | Page 150

Evaluate : (6 – xy) (6 + xy)

Exercise 12 (A) | Q 5.02 | Page 150

Evaluate : (7"x"+2/3"y")(7"x"-2/3"y")

Exercise 12 (A) | Q 5.03 | Page 150

Evaluate : ("a"/(2"b")+(2"b")/"a")("a"/(2"b")-(2"b")/"a")

Exercise 12 (A) | Q 5.04 | Page 150

Evaluate : (3"x"-1/(2"y"))(3"x"+1/(2"y"))

Exercise 12 (A) | Q 5.05 | Page 150

Evaluate : (2a +3) (2a − 3) (4a2 + 9)

Exercise 12 (A) | Q 5.06 | Page 150

Evaluate : (a + bc) (a − bc) (a2 + b2c2)

Exercise 12 (A) | Q 5.07 | Page 150

Evaluate : (5x + 8y) (3x + 5y)

Exercise 12 (A) | Q 5.08 | Page 150

Evaluate : (7x + 15y) (5x − 4y)

Exercise 12 (A) | Q 5.09 | Page 150

Evaluate : (2a − 3b) (3a + 4b)

Exercise 12 (A) | Q 5.1 | Page 150

Evaluate : (9a − 7b) (3a − b)

Exercise 12 (B) [Page 152]

### Selina solutions for Concise Mathematics Class 8 ICSE Chapter 12 Identities Exercise 12 (B) [Page 152]

Exercise 12 (B) | Q 1.1 | Page 152

Expand : (2a + b)2

Exercise 12 (B) | Q 1.2 | Page 152

Expand : (a – 2b)2

Exercise 12 (B) | Q 1.3 | Page 152

Expand : ("a"+1/(2"a"))^2

Exercise 12 (B) | Q 1.4 | Page 152

Expand : (2"a"-1/"a")^2

Exercise 12 (B) | Q 1.5 | Page 152

Expand : (a+b−c)2

Exercise 12 (B) | Q 1.6 | Page 152

Expand : (a−b+c)2

Exercise 12 (B) | Q 1.7 | Page 152

Expand : (3"x"+1/(3"x"))^2

Exercise 12 (B) | Q 1.8 | Page 152

Expand : (2"x"-1/(2"x"))^2

Exercise 12 (B) | Q 2.01 | Page 152

Find the square of x+ 3y

Exercise 12 (B) | Q 2.02 | Page 152

Find the square of 2x − 5y

Exercise 12 (B) | Q 2.03 | Page 152

Find the square of  "a"+1/(5"a")

Exercise 12 (B) | Q 2.04 | Page 152

Find the square of  2"a"-1/"a"

Exercise 12 (B) | Q 2.05 | Page 152

Find the square of  x − 2y +1

Exercise 12 (B) | Q 2.06 | Page 152

Find the square of  3a − 2b − 5c

Exercise 12 (B) | Q 2.07 | Page 152

Find the square of 2"x"+1/"x"+1

Exercise 12 (B) | Q 2.08 | Page 152

Find the square of 5-"x"+2/"x"

Exercise 12 (B) | Q 2.09 | Page 152

Find the square of 2x − 3y + z

Exercise 12 (B) | Q 2.1 | Page 152

Find the square of "x"+1/"x"-1

Exercise 12 (B) | Q 3.1 | Page 152

Evaluate using the expansion of (a + b)2 or (a – b)2 :
(208)2

Exercise 12 (B) | Q 3.2 | Page 152

Evaluate using the expansion of (a + b)2 or (a – b)2 :
(92)2

Exercise 12 (B) | Q 3.3 | Page 152

Evaluate using the expansion of (a + b)2 or (a – b)2 :
(415)2

Exercise 12 (B) | Q 3.4 | Page 152

Evaluate using the expansion of (a + b)2 or (a – b)2 :
(188)2

Exercise 12 (B) | Q 3.5 | Page 152

Evaluate using the expansion of (a + b)2 or (a – b)2 :
(9.4)2

Exercise 12 (B) | Q 3.6 | Page 152

Evaluate using the expansion of (a + b)2 or (a – b)2 :
(20.7)2

Exercise 12 (B) | Q 4.1 | Page 152

Expand : (2a + b)3

Exercise 12 (B) | Q 4.2 | Page 152

Expand : (a − 2b)3

Exercise 12 (B) | Q 4.3 | Page 152

Expand : (3x − 2y)3

Exercise 12 (B) | Q 4.4 | Page 152

Expand : (x + 5y)3

Exercise 12 (B) | Q 4.5 | Page 152

Expand : ("a"+1/"a")^3

Exercise 12 (B) | Q 4.6 | Page 152

Expand : (2"a"-1/(2"a"))^3

Exercise 12 (B) | Q 5.1 | Page 152

Find the cube of: a + 2

Exercise 12 (B) | Q 5.2 | Page 152

Find the cube of: 2a − 1

Exercise 12 (B) | Q 5.3 | Page 152

Find the cube of: 2a + 3b

Exercise 12 (B) | Q 5.4 | Page 152

Find the cube of: 3b − 2a

Exercise 12 (B) | Q 5.5 | Page 152

Find the cube of: 2"x"+1/"x"

Exercise 12 (B) | Q 5.6 | Page 152

Find the cube of: "x"-1/2

Exercise 12 (C) [Pages 154 - 155]

### Selina solutions for Concise Mathematics Class 8 ICSE Chapter 12 Identities Exercise 12 (C) [Pages 154 - 155]

Exercise 12 (C) | Q 1 | Page 154

If a+b=5 and ab = 6, find a2 + b2

Exercise 12 (C) | Q 2 | Page 154

If a – b = 6 and ab = 16, find a2 + b2

Exercise 12 (C) | Q 3.1 | Page 154

If a2 + b2 = 29 and ab = 10, find : a + b

Exercise 12 (C) | Q 3.2 | Page 154

If a2 + b2 = 29 and ab = 10, find : a − b

Exercise 12 (C) | Q 4.1 | Page 154

If a2 + b2= 10 and ab = 3; find :  a – b

Exercise 12 (C) | Q 4.2 | Page 154

If a2 + b2= 10 and ab = 3; find :  a + b

Exercise 12 (C) | Q 5 | Page 154

If "a"  + 1/"a"=3, find "a"^2+1/"a"^2

Exercise 12 (C) | Q 6 | Page 154

If "a"  - 1/"a"=4, find : "a"^2+1/"a"^2

Exercise 12 (C) | Q 7 | Page 154

If "a"^2+ 1/"a"^2=23, find : "a"  +1/"a"

Exercise 12 (C) | Q 8 | Page 154

If "a"^2+ 1/"a"^2=11, find : "a"  -1/"a"

Exercise 12 (C) | Q 9 | Page 155

If a + b + c = 10 and a2 + b2 + c2 = 38, find : ab + bc + ca

Exercise 12 (C) | Q 10 | Page 155

Find : a2 + b2 + c2, if a + b + c = 9 and ab + bc + ca = 24

Exercise 12 (C) | Q 11 | Page 155

Find : a + b + c, if a2 + b2 + c2 = 83 and ab + bc + ca = 71.

Exercise 12 (C) | Q 12 | Page 155

If a + b = 6 and ab=8, find : a3 + b3.

Exercise 12 (C) | Q 13 | Page 155

If a – b = 3 and ab = 10, find : a3 – b3.

Exercise 12 (C) | Q 14 | Page 155

Find : "a"^3+1/"a"^3, if "a"  +1/"a"=5.

Exercise 12 (C) | Q 15 | Page 155

Find : "a"^3-1/"a"^3, if "a" -1/"a"=4.

Exercise 12 (C) | Q 16.1 | Page 155

If 2"x"-1/(2"x")=4, find : 4"x"^2+1/(4"x"^2)

Exercise 12 (C) | Q 16.2 | Page 155

If 2"x"-1/(2"x")=4, find : 8"x"^3-1/(8"x"^3)

Exercise 12 (C) | Q 17.1 | Page 155

If 3"x"+1/(3"x")=3, find : 9"x"^2+1/(9"x"^2)

Exercise 12 (C) | Q 17.2 | Page 155

If 3"x"+1/(3"x")=3, find : 27"x"^3+1/(27"x"^3)

Exercise 12 (C) | Q 18 | Page 155

The sum of the squares of two numbers is 13 and their product is 6. Find:
(i) the sum of the two numbers.
(ii) the difference between them.

Exercise 12 (D) [Page 155]

### Selina solutions for Concise Mathematics Class 8 ICSE Chapter 12 Identities Exercise 12 (D) [Page 155]

Exercise 12 (D) | Q 1.1 | Page 155

Evaluate: (3"x"+1/2)(2"x"+1/3)

Exercise 12 (D) | Q 1.2 | Page 155

Evaluate: (2a + 0.5) (7a − 0.3)

Exercise 12 (D) | Q 1.3 | Page 155

Evaluate: (9 − y) (7 + y)

Exercise 12 (D) | Q 1.4 | Page 155

Evaluate: (2 − z) (15 − z)

Exercise 12 (D) | Q 1.5 | Page 155

Evaluate: (a2 + 5) (a2 − 3)

Exercise 12 (D) | Q 1.6 | Page 155

Evaluate: (4 − ab) (8 + ab)

Exercise 12 (D) | Q 1.7 | Page 155

Evaluate: (5xy − 7) (7xy + 9)

Exercise 12 (D) | Q 1.8 | Page 155

Evaluate: (3a2 − 4b2) (8a2 − 3b2)

Exercise 12 (D) | Q 2.01 | Page 155

Evaluate: (2"x"-3/5)(2"x"+3/5)

Exercise 12 (D) | Q 2.02 | Page 155

Evaluate: (4/7"a"+3/4"b")(4/7"a"-3/4"b")

Exercise 12 (D) | Q 2.03 | Page 155

Evaluate: (6 − 5xy) (6 + 5xy)

Exercise 12 (D) | Q 2.04 | Page 155

Evaluate: (2"a"+1/"2a")(2"a"-1/"2a")

Exercise 12 (D) | Q 2.05 | Page 155

Evaluate: (4x2 − 5y2) (4x2 + 5y2)

Exercise 12 (D) | Q 2.06 | Page 155

Evaluate: (1.6x + 0.7y) (1.6x − 0.7y)

Exercise 12 (D) | Q 2.07 | Page 155

Evaluate: (m + 3) (m − 3) (m2 + 9)

Exercise 12 (D) | Q 2.08 | Page 155

Evaluate: (3x + 4y) (3x − 4y) (9x2 + 16y2)

Exercise 12 (D) | Q 2.09 | Page 155

Evaluate: (a + bc) (a − bc) (a2 + b2c2)

Exercise 12 (D) | Q 2.1 | Page 155

Evaluate: 203 × 197

Exercise 12 (D) | Q 2.11 | Page 155

Evaluate: 20.8 × 19.2

Exercise 12 (D) | Q 3.1 | Page 155

Find the square of 3"x"+2/"y"

Exercise 12 (D) | Q 3.2 | Page 155

Find the square of "5a"/"6b"-"6b"/"5a"

Exercise 12 (D) | Q 3.3 | Page 155

Find the square of 2"m"^2-2/3"n"^2

Exercise 12 (D) | Q 3.4 | Page 155

Find the square of 5"x"+1/(5"x")

Exercise 12 (D) | Q 3.5 | Page 155

Find the square of 8"x"+3/2"y"

Exercise 12 (D) | Q 3.6 | Page 155

Find the square of 607

Exercise 12 (D) | Q 3.7 | Page 155

Find the square of 391

Exercise 12 (D) | Q 3.8 | Page 155

Find the square of 9.7

Exercise 12 (D) | Q 4.1 | Page 155

If  "a"  +1/"a"=2, find : "a"^2+1/"a"^2

Exercise 12 (D) | Q 4.2 | Page 155

If  "a"  +1/"a"=2, find : "a"^4+1/"a"^4

Exercise 12 (D) | Q 5.1 | Page 155

If  "m"  -1/"m"=5, find : "m"^2+1/"m"^2

Exercise 12 (D) | Q 5.2 | Page 155

If  "m"  -1/"m"=5, find : "m"^4+1/"m"^4

Exercise 12 (D) | Q 5.3 | Page 155

If "m"  -1/"m"=5, find : "m"^2-1/"m"^2

Exercise 12 (D) | Q 6.1 | Page 155

If a2 + b2 = 41 and ab = 4, find : a – b

Exercise 12 (D) | Q 6.2 | Page 155

If a2 + b2 = 41 and ab = 4, find : a + b

Exercise 12 (D) | Q 7.1 | Page 155

If 2"a"+1/(2"a")=8, find : 4"a"^2+1/(4"a"^2)

Exercise 12 (D) | Q 7.2 | Page 155

If 2"a"+1/(2"a")=8, find : 16"a"^4+1/(16"a"^4)

Exercise 12 (D) | Q 8.1 | Page 155

If 3"x"-1/(3"x")=5, find : 9"x"^2+1/(9"x"^2)

Exercise 12 (D) | Q 8.2 | Page 155

If 3"x"-1/(3"x")=5, find : 81"x"^4+1/(81"x"^4)

Exercise 12 (D) | Q 9.1 | Page 155

Expand : (3x – 4y + 5z)2

Exercise 12 (D) | Q 9.2 | Page 155

Expand : (2a – 5b – 4c)2

Exercise 12 (D) | Q 9.3 | Page 155

Expand : (5x + 3y)3

Exercise 12 (D) | Q 9.4 | Page 155

Expand : (6a – 7b)3

Exercise 12 (D) | Q 10 | Page 155

If a + b + c = 9 and ab + bc + ca = 15, find: a2 + b2 + c2.

Exercise 12 (D) | Q 11 | Page 155

If a + b + c = 11 and a2 + b2 + c2 = 81, find : ab + bc + ca.

Exercise 12 (D) | Q 12 | Page 155

If 3x – 4y = 5 and xy = 3, find : 27x3 – 64y3.

Exercise 12 (D) | Q 13 | Page 155

If a + b = 8 and ab = 15, find : a3 + b3.

Exercise 12 (D) | Q 14 | Page 155

If 3x + 2y = 9 and xy = 3, find : 27x3 + 8y3.

Exercise 12 (D) | Q 15 | Page 155

If 5x – 4y = 7 and xy = 8, find : 125x3 – 64y3.

Exercise 12 (D) | Q 16 | Page 155

The difference between the two numbers is 5 and their products are 14. Find the difference between their cubes.

## Chapter 12: Identities

Exercise 12 (A)Exercise 12 (B)Exercise 12 (C)Exercise 12 (D)

## Selina solutions for Concise Mathematics Class 8 ICSE chapter 12 - Identities

Selina solutions for Concise Mathematics Class 8 ICSE chapter 12 (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 CISCE Concise Mathematics Class 8 ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Concise Mathematics Class 8 ICSE chapter 12 Identities are Algebraic Identities, Product of Sum and Difference of Two Terms, Important Formula of Expansion, Cubes of Binomials, Application of Formulae, Expansion Form of Numbers.

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