Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 7th

# Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 3 Answers Guide chapter 3 - Algebra [Latest edition]

## Chapter 3: Algebra

Exercise 3.1Exercise 3.2Exercise 3.3
Exercise 3.1 [Pages 61 - 62]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 3 Answers Guide Chapter 3 AlgebraExercise 3.1 [Pages 61 - 62]

#### Fill in the blanks

Exercise 3.1 | Q 1. (i) | Page 61

(p – q)2 = _______________

Exercise 3.1 | Q 1. (ii) | Page 61

The product of (x + 5) and (x – 5) is ____________

Exercise 3.1 | Q 1. (iii) | Page 61

The factors of x2 – 4x + 4 are __________

Exercise 3.1 | Q 1. (iv) | Page 61

Express 24ab2c2 as product of its factors is ___________

#### Say whether the following statements are True or False

Exercise 3.1 | Q 2. (i) | Page 61

(7x + 3)(7x – 4) = 49x2 – 7x – 12

• True

• False

Exercise 3.1 | Q 2. (ii) | Page 61

(a – 1)2 = a2 – 1

• True

• False

Exercise 3.1 | Q 2. (iii) | Page 61

(x2 + y2)(y2 + x2) = (x2 + y2)2

• True

• False

Exercise 3.1 | Q 2. (iv) | Page 61

2p is the factor of 8pq

• True

• False

Exercise 3.1 | Q 3. (i) | Page 61

Express the following as the product of its factor

24 ab2c2

Exercise 3.1 | Q 3. (ii) | Page 61

Express the following as the product of its factor

36 x3y2z

Exercise 3.1 | Q 3. (iii) | Page 61

Express the following as the product of its factor

56 mn2p2

Exercise 3.1 | Q 4. (i) | Page 61

Using the identity (x + a)(x + b) = x2 + x(a + b) + ab, find the following product

(x + 3)(x + 7)

Exercise 3.1 | Q 4. (ii) | Page 61

Using the identity (x + a)(x + b) = x2 + x(a + b) + ab, find the following product

(6a + 9)(6a – 5)

Exercise 3.1 | Q 4. (iii) | Page 61

Using the identity (x + a)(x + b) = x2 + x(a + b) + ab, find the following product

(4x + 3y)(4x + 5y)

Exercise 3.1 | Q 4. (iv) | Page 61

Using the identity (x + a)(x + b) = x2 + x(a + b) + ab, find the following product

(8 + pq)(pq + 7)

Exercise 3.1 | Q 5. (i) | Page 62

Expand the following square, using suitable identities

(2x + 5)2

Exercise 3.1 | Q 5. (ii) | Page 62

Expand the following square, using suitable identities

(b – 7)2

Exercise 3.1 | Q 5. (iii) | Page 62

Expand the following square, using suitable identities

(mn + 3p)2

Exercise 3.1 | Q 5. (iv) | Page 62

Expand the following square, using suitable identities

(xyz – 1)2

Exercise 3.1 | Q 6. (i) | Page 62

Using the identity (a + b)(a – b) = a2 – b2, find the following product

(p + 2)(p – 2)

Exercise 3.1 | Q 6. (ii) | Page 62

Using the identity (a + b)(a – b) = a2 – b2, find the following product

(1 + 3b)(3b – 1)

Exercise 3.1 | Q 6. (iii) | Page 62

Using the identity (a + b)(a – b) = a2 – b2, find the following product

(4 – mn)(mn + 4)

Exercise 3.1 | Q 6. (iv) | Page 62

Using the identity (a + b)(a – b) = a2 – b2, find the following product

(6x + 7y)(6x – 7y)

Exercise 3.1 | Q 7. (i) | Page 62

Evaluate the following, using suitable identity

512

Exercise 3.1 | Q 7. (ii) | Page 62

Evaluate the following, using suitable identity

1032

Exercise 3.1 | Q 7. (iii) | Page 62

Evaluate the following, using suitable identity

9982

Exercise 3.1 | Q 7. (iv) | Page 62

Evaluate the following, using suitable identity

472

Exercise 3.1 | Q 7. (v) | Page 62

Evaluate the following, using suitable identity

297 × 303

Exercise 3.1 | Q 7. (vi) | Page 62

Evaluate the following, using suitable identity

990 × 1010

Exercise 3.1 | Q 7. (vii) | Page 62

Evaluate the following, using suitable identity

51 × 52

Exercise 3.1 | Q 8 | Page 62

Simplify: (a + b)2 – 4ab

Exercise 3.1 | Q 9 | Page 62

Show that (m – n)2 + (m + n)2 = 2(m2 + n2)

Exercise 3.1 | Q 10 | Page 62

If a + b = 10 and ab = 18, find the value of a2 + b2

Exercise 3.1 | Q 11. (i) | Page 62

Factorise the following algebraic expression by using the identity a2 – b2 = (a + b)(a – b)

z2 – 16

Exercise 3.1 | Q 11. (ii) | Page 62

Factorise the following algebraic expression by using the identity a2 – b2 = (a + b)(a – b)

9 – 4y2

Exercise 3.1 | Q 11. (iii) | Page 62

Factorise the following algebraic expression by using the identity a2 – b2 = (a + b)(a – b)

25a2 – 49b2

Exercise 3.1 | Q 11. (iv) | Page 62

Factorise the following algebraic expression by using the identity a2 – b2 = (a + b)(a – b)

x4 – y4

Exercise 3.1 | Q 12. (i) | Page 62

Factorise the following using suitable identity

x2 – 8x + 16

Exercise 3.1 | Q 12. (ii) | Page 62

Factorise the following using suitable identity

y2 + 20y + 100

Exercise 3.1 | Q 12. (iii) | Page 62

Factorise the following using suitable identity

36m2 + 60m + 25

Exercise 3.1 | Q 12. (iv) | Page 62

Factorise the following using suitable identity

64x2 – 112xy + 49y2

Exercise 3.1 | Q 12. (v) | Page 62

Factorise the following using suitable identity

a2 + 6ab + 9b2 – c2

#### Objective Type Questions

Exercise 3.1 | Q 13 | Page 62

If a + b = 5 and a2 + b2 = 13, then ab = ?

• 12

• 6

• 5

• 13

Exercise 3.1 | Q 14 | Page 62

(5 + 20)(–20 – 5) = ?

• − 425

• 375

• − 625

• 0

Exercise 3.1 | Q 15 | Page 62

The factors of x2 – 6x + 9 are

• (x – 3)(x – 3)

• (x – 3)(x + 3)

• (x + 3)(x + 3)

• (x – 6)(x + 9)

Exercise 3.1 | Q 16 | Page 62

The common factors of the algebraic expression ax2y, bxy2 and cxyz is

• x2y

• xy2

• xyz

• xy

Exercise 3.2 [Pages 68 - 69]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 3 Answers Guide Chapter 3 AlgebraExercise 3.2 [Pages 68 - 69]

Exercise 3.2 | Q 1. (i) | Page 68

Given that x ≥ y. Fill in the blank with suitable inequality sign

y square x

Exercise 3.2 | Q 1. (ii) | Page 68

Given that x ≥ y. Fill in the blank with suitable inequality sign

x + 6 square y + 6

Exercise 3.2 | Q 1. (iii) | Page 68

Given that x ≥ y. Fill in the blank with suitable inequality sign

x2 square xy

Exercise 3.2 | Q 1. (iv) | Page 68

Given that x ≥ y. Fill in the blank with suitable inequality sign

– xy square – y2

Exercise 3.2 | Q 1. (v) | Page 68

Given that x ≥ y. Fill in the blank with suitable inequality sign

x – y square 0

#### Say True or False

Exercise 3.2 | Q 2. (i) | Page 68

Linear inequation has almost one solution

• True

• False

Exercise 3.2 | Q 2. (ii) | Page 68

When x is an integer, the solution set for x ≤ 0 are −1, −2, ...

• True

• False

Exercise 3.2 | Q 2. (iii) | Page 68

An inequation, −3 < x < −1, where x is an integer, cannot be represented in the number line

• True

• False

Exercise 3.2 | Q 2. (iv) | Page 68

x < − y can be rewritten as – y < x

• True

• False

Exercise 3.2 | Q 3. (i) | Page 68

Solve the following inequation

x ≤ 7, where x is a natural number

Exercise 3.2 | Q 3. (ii) | Page 68

Solve the following inequation

x – 6 < 1, where x is a natural number

Exercise 3.2 | Q 3. (iii) | Page 68

Solve the following inequation

2a + 3 ≤ 13, where a is a whole number

Exercise 3.2 | Q 3. (iv) | Page 68

Solve the following inequation

6x – 7 ≥ 35, where x is an integer

Exercise 3.2 | Q 3. (v) | Page 68

Solve the following inequation

4x – 9 > – 33, where x is a negative integer

Exercise 3.2 | Q 4. (i) | Page 68

Solve the following inequation and represent the solution on the number line:

k > −5, k is an integer

Exercise 3.2 | Q 4. (ii) | Page 68

Solve the following inequation and represent the solution on the number line:

−7 ≤ y, y is a negative integer

Exercise 3.2 | Q 4. (iii) | Page 68

Solve the following inequation and represent the solution on the number line:

−4 ≤ x ≤ 8, x is a natural number.

Exercise 3.2 | Q 4. (iv) | Page 68

Solve the following inequation and represent the solution on the number line:

3m – 5 ≤ 2m + 1, m is an integer

Exercise 3.2 | Q 5 | Page 69

An artist can spend any amount between ₹ 80 to ₹ 200 on brushes. If cost of each brush is ₹ 5 and there are 6 brushes in each packet, then how many packets of brush can the artist buy?

#### Objective Type Questions

Exercise 3.2 | Q 6 | Page 69

The solutions set of the inequation 3 ≤ p ≤ 6 are (where p is a natural number)

• 4, 5 and 6

• 3, 4 and 5

• 4 and 5

• 3, 4, 5 and 6

Exercise 3.2 | Q 7 | Page 69

The solution of the inequation 5x + 5 ≤ 15 are (where x is a natural number)

• 1 and 2

• 0, 1 and 2

• 2, 1, 0, −1, −2

• 1, 2, 3..

Exercise 3.2 | Q 8 | Page 69

The cost of one pen is ₹ 8 and it is available in a sealed pack of 10 pens. If Swetha has only ₹ 500, how many packs of pens can she buy at the maximum?

• 10

• 5

• 6

• 8

Exercise 3.2 | Q 9 | Page 69

The inequation that is represented on the number line as shown below is ____________

• −4 < x < 0

• −4 ≤ x ≤ 0

• −4 < x ≤ 0

• −4 ≤ x < 0

Exercise 3.3 [Pages 69 - 70]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 3 Answers Guide Chapter 3 AlgebraExercise 3.3 [Pages 69 - 70]

#### Miscellaneous Practice problems

Exercise 3.3 | Q 1. (i) | Page 69

Using identity, find the value of (4.9)2

Exercise 3.3 | Q 1. (ii) | Page 69

Using identity, find the value of (100.1)2

Exercise 3.3 | Q 1. (iii) | Page 69

Using identity, find the value of (1.9) × (2.1)

Exercise 3.3 | Q 2 | Page 69

Factorise: 4x2 – 9y2

Exercise 3.3 | Q 3. (i) | Page 69

Simplify using identities

(3p + q)(3p + r)

Exercise 3.3 | Q 3. (ii) | Page 69

Simplify using identities

(3p + q)(3p – q)

Exercise 3.3 | Q 4 | Page 69

Show that (x + 2y)2 – (x – 2y)2 = 8xy

Exercise 3.3 | Q 5 | Page 69

The pathway of a square paddy field has 5 m width and length of its side is 40 m. Find the total area of its pathway. (Note: Use suitable identity)

#### Challenge Problems

Exercise 3.3 | Q 6 | Page 69

If X = a2 – 1 and Y = 1 – b2, then find X + Y and factorize the same

Exercise 3.3 | Q 7 | Page 69

Find the value of (x – y)(x + y)(x2 + y2)

Exercise 3.3 | Q 8 | Page 70

Simplify (5x – 3y)2 – (5x + 3y)2

Exercise 3.3 | Q 9. (i) | Page 70

Simplify: (a + b)2 – (a – b)2

Exercise 3.3 | Q 9. (ii) | Page 70

Simplify: (a + b)2 + (a – b)2

Exercise 3.3 | Q 10 | Page 70

A square lawn has a 2 m wide path surrounding it. If the area of the path is 136 m2, find the area of lawn

Exercise 3.3 | Q 11. (i) | Page 70

Solve the following inequalities

4n + 7 ≥ 3n + 10, n is an integer

Exercise 3.3 | Q 11. (ii) | Page 70

Solve the following inequalities

6(x + 6) ≥ 5(x – 3), x is a whole number

Exercise 3.3 | Q 11. (iii) | Page 70

Solve the following inequalities

−13 ≤ 5x + 2 ≤ 32, x is an integer

## Chapter 3: Algebra

Exercise 3.1Exercise 3.2Exercise 3.3

## Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 3 Answers Guide chapter 3 - Algebra

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Concepts covered in Class 7th Mathematics Term 3 Answers Guide chapter 3 Algebra are Concept of Identity, Geometrical Approach to Multiplication of Monomials, Expansion of (x + a)(x + b), Expansion of (a + b)2 = a2 + 2ab + b2, Expansion of (a - b)2 = a2 - 2ab + b2, Expansion of (a + b)(a - b), Inequation, Solving Linear Inequations, Graphical Representation of Inequation.

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