#### Chapters

## Chapter 3: Algebra

### 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

(p – q)^{2} = _______________

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

The factors of x^{2} – 4x + 4 are __________

Express 24ab^{2}c^{2} as product of its factors is ___________

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

(7x + 3)(7x – 4) = 49x^{2} – 7x – 12

True

False

(a – 1)^{2} = a^{2} – 1

True

False

(x^{2} + y^{2})(y^{2} + x^{2}) = (x^{2} + y^{2})^{2}

True

False

2p is the factor of 8pq

True

False

Express the following as the product of its factor

24 ab^{2}c^{2}

Express the following as the product of its factor

36 x^{3}y^{2}z

Express the following as the product of its factor

56 mn^{2}p^{2}

Using the identity (x + a)(x + b) = x^{2} + x(a + b) + ab, find the following product

(x + 3)(x + 7)

Using the identity (x + a)(x + b) = x^{2} + x(a + b) + ab, find the following product

(6a + 9)(6a – 5)

Using the identity (x + a)(x + b) = x^{2} + x(a + b) + ab, find the following product

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

Using the identity (x + a)(x + b) = x^{2} + x(a + b) + ab, find the following product

(8 + pq)(pq + 7)

Expand the following square, using suitable identities

(2x + 5)^{2}

Expand the following square, using suitable identities

(b – 7)^{2}

Expand the following square, using suitable identities

(mn + 3p)^{2}

Expand the following square, using suitable identities

(xyz – 1)^{2}

Using the identity (a + b)(a – b) = a^{2} – b^{2}, find the following product

(p + 2)(p – 2)

Using the identity (a + b)(a – b) = a^{2} – b^{2}, find the following product

(1 + 3b)(3b – 1)

Using the identity (a + b)(a – b) = a^{2} – b^{2}, find the following product

(4 – mn)(mn + 4)

Using the identity (a + b)(a – b) = a^{2} – b^{2}, find the following product

(6x + 7y)(6x – 7y)

Evaluate the following, using suitable identity

51^{2}

Evaluate the following, using suitable identity

103^{2}

Evaluate the following, using suitable identity

998^{2}

Evaluate the following, using suitable identity

47^{2}

Evaluate the following, using suitable identity

297 × 303

Evaluate the following, using suitable identity

990 × 1010

Evaluate the following, using suitable identity

51 × 52

Simplify: (a + b)^{2} – 4ab

Show that (m – n)^{2} + (m + n)^{2} = 2(m^{2} + n^{2})

If a + b = 10 and ab = 18, find the value of a^{2} + b^{2}

Factorise the following algebraic expression by using the identity a^{2} – b^{2} = (a + b)(a – b)

z^{2} – 16

Factorise the following algebraic expression by using the identity a^{2} – b^{2} = (a + b)(a – b)

9 – 4y^{2}

Factorise the following algebraic expression by using the identity a^{2} – b^{2} = (a + b)(a – b)

25a^{2} – 49b^{2}

Factorise the following algebraic expression by using the identity a^{2} – b^{2} = (a + b)(a – b)

x^{4} – y^{4}

Factorise the following using suitable identity

x^{2} – 8x + 16

Factorise the following using suitable identity

y^{2} + 20y + 100

Factorise the following using suitable identity

36m^{2} + 60m + 25

Factorise the following using suitable identity

64x^{2} – 112xy + 49y^{2}

Factorise the following using suitable identity

a^{2} + 6ab + 9b^{2} – c^{2}

#### Objective Type Questions

If a + b = 5 and a^{2} + b^{2} = 13, then ab = ?

12

6

5

13

(5 + 20)(–20 – 5) = ?

− 425

375

− 625

0

The factors of x^{2} – 6x + 9 are

(x – 3)(x – 3)

(x – 3)(x + 3)

(x + 3)(x + 3)

(x – 6)(x + 9)

The common factors of the algebraic expression ax^{2}y, bxy^{2} and cxyz is

x

^{2}yxy

^{2}xyz

xy

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

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

y `square` x

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

x + 6 `square` y + 6

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

x^{2} `square` xy

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

– xy `square` – y^{2}

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

x – y `square` 0

#### Say True or False

Linear inequation has almost one solution

True

False

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

True

False

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

True

False

x < − y can be rewritten as – y < x

True

False

Solve the following inequation

x ≤ 7, where x is a natural number

Solve the following inequation

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

Solve the following inequation

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

Solve the following inequation

6x – 7 ≥ 35, where x is an integer

Solve the following inequation

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

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

k > −5, k is an integer

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

−7 ≤ y, y is a negative integer

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

−4 ≤ x ≤ 8, x is a natural number.

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

3m – 5 ≤ 2m + 1, m is an integer

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

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

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..

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

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

### 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

Using identity, find the value of (4.9)^{2}

Using identity, find the value of (100.1)^{2}

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

Factorise: 4x^{2} – 9y^{2}

Simplify using identities

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

Simplify using identities

(3p + q)(3p – q)

Show that (x + 2y)^{2} – (x – 2y)^{2} = 8xy

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

If X = a^{2} – 1 and Y = 1 – b^{2}, then find X + Y and factorize the same

Find the value of (x – y)(x + y)(x^{2} + y^{2})

Simplify (5x – 3y)^{2} – (5x + 3y)^{2}

Simplify: (a + b)^{2} – (a – b)^{2}

Simplify: (a + b)^{2} + (a – b)^{2}

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

Solve the following inequalities

4n + 7 ≥ 3n + 10, n is an integer

Solve the following inequalities

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

Solve the following inequalities

−13 ≤ 5x + 2 ≤ 32, x is an integer

## Chapter 3: Algebra

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

Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 3 Answers Guide chapter 3 (Algebra) 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 Tamil Nadu Board of Secondary Education Class 7th Mathematics Term 3 Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

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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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