## RS Aggarwal Class 8 Solutions Chapter 7 Factorisation Ex 7B

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7B.

**Other Exercises**

- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7A
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7B
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7C
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7D
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7E

**Question 1.**

**Solution:**

x^{2} – 36

= (x)^{2} – (6)^{2} { ∵ a^{2} – b^{2} = (a + b) (a – b)}

= (x + 6) (x – 6) Ans.

**Question 2.**

**Solution:**

4a^{2} – 9

= (2a)^{2} – (3)^{2}

= (2a + 3) (2a – 3)

{ ∵ a^{2} – b^{2} = (a + b) (a – b)}

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**Question 3.**

**Solution:**

81 – 49x^{2}

= (9)^{2} – (7x)^{2}

= (9 + 7x) (9 – 7x) { ∵ a^{2} – b^{2} = (a + b) (a – b)}

**Question 4.**

**Solution:**

= (2x)^{2} – (3y)^{2}

= (2x + 3y)(2x-3y)

{∵ a^{2} – b^{2} = (a + b) (a – b)}

**Question 5.**

**Solution:**

Using a^{2} – b^{2}

= (a + b) (a – b)

= 16a^{2} – 225b^{2}

= (4a)^{2} – (15b)^{2}

= (4a + 15b) (4b – 5b)

**Question 6.**

**Solution:**

Using a^{2} – b^{2}

= (a + b) (a – b)

= (3ab)^{2} – (5)^{2}

= (3ab + 5) (3ab – 5)

**Question 7.**

**Solution:**

Using a^{2} – b^{2} = (a + b) (a – b)

16a^{2} – 144 = (4a)^{2} = (12)^{2}

= (4a + 12) (4a – 12)

= 4 (a + 3) x 4 (a – 3)

= 16 (a + 3) (a – 3)

**Question 8.**

**Solution:**

63a^{2} – 112b^{2}

= 7 (9a^{2} – 16b^{2})

= 7 [(3a)^{2} – (4b)^{2}

= 7 (3a + 4b) (3a – 4b)

**Question 9.**

**Solution:**

20a^{2} – 45b^{2}

= 5 {4a^{2} – 9b^{2}}

= 5{(2a)^{2} – (3b)^{2})

= 5(2a + 3b) (2a – 3b) Ans.

**Question 10.**

**Solution:**

12x^{2} – 27

= 3(4x^{2} – 9)

= 3{(2x)^{2} – (3)^{2}}

= 3(2x + 3) (2x – 3) Ans.

**Question 11.**

**Solution:**

x^{3} – 64x

= x(x^{2} – 64)

= x{(x)^{2} – (8)^{2}}

= x(x + 8) (x – 8) Ans.

**Question 12.**

**Solution:**

16x^{5} – 144x^{3}

= 16x^{3} [x^{2} – 9]

= 16x^{3} [(x)^{2} – (3)^{2}]

= 16x^{3} (x + 3) (x – 3)

**Question 13.**

**Solution:**

3x^{5} – 48x^{3}

= 3x^{3} {x^{2} – 16}

= 3x^{3}{(x)^{2} – (4)^{2}}

= 3x^{3} (x + 4) (x – 4) Ans.

**Question 14.**

**Solution:**

16p^{3} – 4p

= 4p [4p^{2} – 1]

= 4p ((2p)^{2} – (1)^{2}]

= 4p(2p + 1)(2p – 1)

**Question 15.**

**Solution:**

63a^{2}b^{2} – 7

= 7(9a^{2}b^{2} – 1)

= 7{(3ab)^{2} – (1)^{2})

= 7(3ab + 1) (3ab – 1) Ans.

**Question 16.**

**Solution:**

1 – (b – c)^{2}

= (1)^{2} – (b – c)^{2}

= (1 + b + c) (1 – b + c) Ans.

{ ∵ a^{2} – b^{2} = (a + b) (a – b)}

**Question 17.**

**Solution:**

(2a + 3b)^{2} – 16c^{2}

= (2a + 3b)^{2} – (4c)^{2}

=(2a + 3b + 4c)(2a + 3b – 4c)Ans.

{ ∵ a^{2} – b^{2} = (a + b)(a – b)}

**Question 18.**

**Solution:**

(l + m)^{2} – (l – m)^{2}

= (l + m + l – m)(l + m – l + m)

{ ∵ a^{2} – b^{2} = (a + b)(a – b)}

= 2l x 2m = 4lm

**Question 19.**

**Solution:**

(2x + 5y)^{2} – (1)^{2}

=(2x + 5y + 1)(2x + 5y – 1)

{ ∵ a^{2} – b^{2} = (a + b)(a – b)}

**Question 20.**

**Solution:**

36c^{2} – (5a + b)^{2}

= (6c)^{2} – (5a + b)^{2}

{ ∵ a^{2} – b^{2} = (a + b)(a – b)}

= (6c + 5a + b)(6c – 5a – b)

**Question 21.**

**Solution:**

(3x – 4y)^{2} – 25z^{2}

= (3x – 4y)^{2} – (5z)^{2}

= (3x – 4y + 5z) (3x – 4y – 5z) Ans.

**Question 22.**

**Solution:**

x^{2} – y^{2} – 2y – 1

= x^{2} – (y^{2} + 2y + 1)

= (x)^{2} – (y + 1)^{2}

= (x + y + 1)(x – y – 1)Ans.

**Question 23.**

**Solution:**

25 – a^{2} – b^{2} – 2ab

= 25 – (a^{2} + b^{2} + 2ab)

= (5)^{2} – (a + b)^{2}

= (5 + a + b)(5 – a – b)Ans.

**Question 24.**

**Solution:**

25a^{2} – 4b^{2} + 28bc – 49c^{2}

= 25a^{2} – [4b^{2} – 28bc + 49c^{2}]

{ ∵ a^{2} – 2ab + b^{2} = (a – b)^{2}}

= (5a)^{2} – [(2b)^{2} – 2 x 2b x 7c + (7c)^{2}]

= (5a)^{2} – (2b – 7c)^{2}

{ ∵ (a^{2} – b^{2} = (a + b)(a – b)}

= (5a + 2b – 7c) (5a – 2b + 7c)

**Question 25.**

**Solution:**

9a^{2} – b^{2} + 4b – 4

= 9a^{2} – (b^{2} – 4b + 4)

= (3a)^{2} – [(b)^{2} – 2 x b x 2 + (2)^{2}]

= (3a)^{2} – (b – 2)^{2}

{ ∵ a^{2} – 2ab + b^{2} = (a – b)^{2}}

= (3a + b – 2)(3a – b + 2)

{ ∵ a^{2} – b^{2} = (a + b)(a – b)}

**Question 26.**

**Solution:**

(10)^{2} – (x – 5)^{2}

= (10)^{2} – (x – 5)^{2}

= (10 + x – 5)(10 – x + 5)

= (5 + x) (15 – x) Ans.

**Question 27.**

**Solution:**

{(405)^{2} – (395)^{2}}

= (405)^{2} – (395)^{2}

= (405 + 395) (405 – 395)

{ ∵ a^{2} – b^{2}(a + b) (a – b)}

= 800 x 10 = 8000

**Question 28.**

**Solution:**

(7.8)^{2} – (2.2)^{2}

= (7.8 + 2.2) (7.8 – 2.2)

= 10.0 x 5.6

= 56 Ans.

Hope given RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7B are helpful to complete your math homework.

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