Exercise 3B RS Aggarwal Class 9 Factorisation of Polynomials Best Solutions

Exercise 3B RS Aggarwal Class 9 contains 40 questions. These questions has been solved below. The questions belong to chapter 3 Factorisation of Polynomials.

Exercise 3B RS Aggarwal Class 9 Mathematics Solutions

Q.1 Q.2 Q.3 Q.4 Q.5 Q.6 Q.7 Q.8 Q.9 Q.10 Q.11 Q.12 Q.13 Q.14 Q.15 Q.16 Q.17 Q.18 Q.19 Q.20 Q.21 Q.22 Q.23 Q.24 Q.25 Q.26 Q.27 Q.28 Q.29 Q.30 Q.31 Q.32 Q.33 Q.34 Q.35 Q.36 Q.37 Q.38 Q.39 Q.40

The question number 1 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

Factorise:

1. $9 x^{2} - 16 y^{2}$

Answer

We have
$9 x^{2} - 16 y^{2}$
$= {(3 x)}^{2} - {(4 y)}^{2}$
$= (3 x - 4 y) (3 x + 4 y)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 2 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

2. $(\frac{25}{4} x^{2} - \frac{1}{9} y^{2})$

Answer

We have
$(\frac{25}{4} x^{2} - \frac{1}{9} y^{2})$
$= {(\frac{5}{2} x)}^{2} - {(\frac{1}{3} y)}^{2}$
$= (\frac{5}{2} x - \frac{1}{3} y) (\frac{5}{2} x + \frac{1}{3} y)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 3 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

3. $81 - 16 x^{2}$

Answer

We have
$81 - 16 x^{2}$
$= {(9)}^{2} - {(4 x)}^{2}$
$= (9 - 4 x) (9 + 4 x)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 4 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

4. $5 - 20 x^{2}$

Answer

We have
$5 - 20 x^{2}$
$= 5 [1 - 4 x^{2}]$
$= 5 [1^{2} - {(2 x)}^{2}]$
$= 5 (1 - 2 x) (1 + 2 x)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 5 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

5. $2 x^{4} - 32$

Answer

We have
$2 x^{4} - 32$
$= 2 [x^{4} - 16]$
$= 2 [{(x^{2})}^{2} - 4^{2}]$
$= 2 (x^{2} - 4) (x^{2} + 4)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$
$= 2 (x^{2} - 2^{2}) (x^{2} + 4)$ ... $(∵ 4 = 2^{2})$
$= 2 (x - 2) (x + 2) (x^{2} + 4)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 6 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

6. $3 a^{3} b - 243 a b^{3}$

Answer

We have
$3 a^{3} b - 243 a b^{3}$
$= 3 a b [a^{2} - 81 b^{2}]$
$= 3 a b [a^{2} - {(9 b)}^{2}]$
$= 3 a b (a - 9 b) (a + 9 b)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 7 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

7. $3 x^{3} - 48 x$

Answer

We have
$3 x^{3} - 48 x$
$= 3 x (x^{2} - 16)$
$= 3 x (x^{2} - 4^{2})$
$= 3 x (x - 4) (x + 4)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 8 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

8. $27 a^{2} - 48 b^{2}$

Answer

We have
$27 a^{2} - 48 b^{2}$
$= 3 (9 a^{2} - 16 b^{2})$
$= 3 [{(3 a)}^{2} - {(4 b)}^{2}]$
$= 3 (3 a - 4 b) (3 a + 4 b)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 9 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

9. $x - 64 x^{3}$

Answer

We have
$x - 64 x^{3}$
$= x (1 - 64 x^{2})$
$= x [1^{2} - {(8 x)}^{2}]$
$= x (1 - 8 x) (1 + 8 x)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 10 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

10. $8 a b^{2} - 18 a^{3}$

Answer

We have
$8 a b^{2} - 18 a^{3}$
$= 2 a (4 b^{2} - 9 a^{2})$
$= 2 a [{(2 b)}^{2} - {(3 a)}^{2}]$
$= 2 a (2 b - 3 a) (2 b + 3 a)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 11 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

11. $150 - 6 x^{2}$

Answer

We have
$150 - 6 x^{2}$
$= 6 (25 - x^{2})$
$= 6 (5^{2} - x^{2})$
$= 6 (5 - x) (5 + x)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 12 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

12. $2 - 50 x^{2}$

Answer

We have
$2 - 50 x^{2}$
$= 2 (1 - 25 x^{2})$
$= 2 [1 - {(5 x)}^{2}]$
$= 2 (1 - 5 x) (1 + 5 x)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

The question number 13 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

13. $20 x^{2} - 45$

Answer

We have
$20 x^{2} - 45$
$= 5 (4 x^{2} - 9)$
$= 5 [{(2 x)}^{2} - 3^{2}]$
$= 5 (2 x - 3) (2 x + 3)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

The question number 14 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

14. ${(3 a + 5 b)}^{2} - 4 c^{2}$

Answer

We have
${(3 a + 5 b)}^{2} - 4 c^{2}$
$= [{(3 a + 5 b)}^{2} - {(2 c)}^{2}]$
$= [(3 a + 5 b) - 2 c] [(3 a + 5 b) + 2 c]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

The question number 15 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

15. $a^{2} - b^{2} - a - b$

Answer

We have
$a^{2} - b^{2} - a - b$
$= [(a^{2} - b^{2}) - (a + b)]$
$= [(a - b) (a + b) - (a + b)]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (a + b) [(a - b) - 1]$
$= (a + b) (a - b - 1)$ .

The question number 16 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

16. $4 a^{2} - 9 b^{2} - 2 a - 3 b$

Answer

We have
$4 a^{2} - 9 b^{2} - 2 a - 3 b$
$= [(4 a^{2} - 9 b^{2}) - (2 a + 3 b)]$
$= [{{(2 a)}^{2} - {(3 b)}^{2}} - (2 a + 3 b)]$
$= [{(2 a - 3 b) (2 a + 3 b)} - (2 a + 3 b)]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (2 a + 3 b) [(2 a - 3 b) - 1]$
$= (2 a + 3 b) (2 a - 3 b - 1)$ .

The question number 17 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

17. $a^{2} - b^{2} + 2 b c - c^{2}$

Answer

We have
$a^{2} - b^{2} + 2 b c - c^{2}$
$= a^{2} - (b^{2} - 2 b c + c^{2})$
$= a^{2} - {(b - c)}^{2}$
$= [a - (b - c)] [a + (b - c)]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (a - b + c) (a + b - c)$ .

The question number 18 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

18. $4 a^{2} - 4 b^{2} + 4 a + 1$

Answer

We have
$4 a^{2} - 4 b^{2} + 4 a + 1$
$= 4 a^{2} + 4 a + 1 - 4 b^{2}$
$= (4 a^{2} + 4 a + 1) - 4 b^{2}$
$= {{(2 a)}^{2} + 2 \times 2 a \times 1 + 1^{2}} - {(2 b)}^{2}$
$= {(2 a + 1)}^{2} - {(2 b)}^{2}$
$= [{(2 a + 1) - 2 b} {(2 a + 1) + 2 b}]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= [{2 a + 1 - 2 b} {2 a + 1 + 2 b}]$
$= (2 a - 2 b + 1) (2 a + 2 b + 1)$ .

The question number 19 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

19. $a^{2} + 2 a b + b^{2} - 9 c^{2}$

Answer

We have
$a^{2} + 2 a b + b^{2} - 9 c^{2}$
$= (a^{2} + 2 a b + b^{2}) - 9 c^{2}$
$= {(a + b)}^{2} - {(3 c)}^{2}$
$= [{(a + b) - 3 c} {(a + b) + 3 c}]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= {a + b - 3 c} {a + b + 3 c}$
$= (a + b - 3 c) (a + b + 3 c)$ .

The question number 20 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

20. $108 a^{2} - 3 {(b - c)}^{2}$

Answer

We have
$108 a^{2} - 3 {(b - c)}^{2}$
$= 3 [36 a^{2} - {(b - c)}^{2}]$
$= 3 [{(6 a)}^{2} - {(b - c)}^{2}]$
$= 3 [{6 a - (b - c)} {6 a + (b - c)}]$
$= 3 [{6 a - b + c} {6 a + b - c}]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= 3 (6 a - b + c) (6 a + b - c)$

The question number 21 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

21. ${(a + b)}^{3} - a - b$

Answer

We have
${(a + b)}^{3} - a - b$
$= (a + b) [{(a + b)}^{2} - 1]$
$= (a + b) [{(a + b) - 1} {(a + b) + 1}]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (a + b) (a + b - 1) (a + b + 1)$ .

The question number 22 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

22. $x^{2} + y^{2} - z^{2} - 2 x y$

Answer

We have
$x^{2} + y^{2} - z^{2} - 2 x y$
$= x^{2} + y^{2} - 2 x y - z^{2}$
$= (x^{2} + y^{2} - 2 x y) - z^{2}$
$= [{(x - y)}^{2} - z^{2}]$
$= [{(x - y) - z} {(x - y) + z}]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (x - y - z) (x - y + z)$

The question number 23 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

23. $x^{2} + 2 x y + y^{2} - a^{2} + 2 a b - b^{2}$

Answer

We have
$x^{2} + 2 x y + y^{2} - a^{2} + 2 a b - b^{2}$
$= (x^{2} + 2 x y + y^{2}) - (a^{2} - 2 a b + b^{2})$
$= {(x + y)}^{2} - {(a - b)}^{2}$
$= [{(x + y) - (a - b)} {(x + y) + (a - b)}]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= [{x + y - a + b} {x + y + a - b}]$
$= (x + y - a + b) (x + y + a - b)$ .

The question number 24 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

24. $25 x^{2} - 10 x + 1 - 36 y^{2}$

Answer

We have
$25 x^{2} - 10 x + 1 - 36 y^{2}$
$= (25 x^{2} - 10 x + 1) - 36 y^{2}$
$= {{(5 x)}^{2} - 2 \times 5 x \times 1 + 1^{2}} - 36 y^{2}$
$= [{{(5 x - 1)}^{2} - {(6 y)}^{2}}]$
$= [{(5 x - 1) - (6 y)} {(5 x - 1) + (6 y)}]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (5 x - 1 - 6 y) (5 x - 1 + 6 y)$ .

The question number 25 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

25. $a - b - a^{2} + b^{2}$

Answer

We have
$a - b - a^{2} + b^{2}$
$= (a - b) - (a^{2} - b^{2})$
$= (a - b) - (a - b) (a + b)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (a - b) [1 - (a + b)]$
$= (a - b) (1 - a - b)$

The question number 26 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

26. $a^{2} - b^{2} - 4 a c + 4 c^{2}$

Answer

We have
$a^{2} - b^{2} - 4 a c + 4 c^{2}$
$= a^{2} - 4 a c + 4 c^{2} - b^{2}$
$= (a^{2} - 4 a c + 4 c^{2}) - b^{2}$
$= {a^{2} - 4 a c + {(2 c)}^{2}} - b^{2}$
$= {(a - c)}^{2} - b^{2}$
$= {(a - c) - b} {(a - c) + b}$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (a - c - b) (a - c + b)$ .

The question number 27 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

27. $9 - a^{2} + 2 a b - b^{2}$

Answer

We have
$9 - a^{2} + 2 a b - b^{2}$
$= 9 - (a^{2} - 2 a b + b^{2})$
$= 3^{2} - {(a - b)}^{2}$
$= {3 + (a - b)} {3 - (a - b)}$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (3 + a - b) (3 - a + b)$ .

The question number 28 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

28. $x^{3} - 5 x^{2} - x + 5$

Answer

We have
$x^{3} - 5 x^{2} - x + 5$
$= (x^{3} - 5 x^{2}) - (x - 5)$
$= x^{2} (x - 5) - (x - 5)$
$= (x - 5) (x^{2} - 1)$
$= (x - 5) (x - 1) (x + 1)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

The question number 29 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

29. $1 + 2 a b - (a^{2} + b^{2})$

Answer

We have
$1 + 2 a b - (a^{2} + b^{2})$
$= 1 + 2 a b - a^{2} - b^{2}$
$= 1 - a^{2} - b^{2} + 2 a b$
$= 1 - (a^{2} + b^{2} - 2 a b)$
$= 1^{2} - {(a - b)}^{2}$
$= {1 + (a - b)} {1 - (a - b)}$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (1 + a - b) (1 - a + b)$

The question number 30 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

30. $9 a^{2} + 6 a + 1 - 36 b^{2}$

Answer

We have
$9 a^{2} + 6 a + 1 - 36 b^{2}$
$= (9 a^{2} + 6 a + 1) - 36 b^{2}$
$= [{(3 a)}^{2} + 2 \times 3 a \times 1 + 1^{2}] - 36 b^{2}$
$= [{(3 a + 1)}^{2} - {(6 b)}^{2}]$
$= [{(3 a + 1) + (6 b)} {(3 a + 1) - (6 b)}]$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= [{3 a + 1 + 6 b} {3 a + 1 - 6 b}]$
$= (3 a + 1 + 6 b) (3 a + 1 - 6 b)$

The question number 31 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

31. $x^{2} - y^{2} + 6 y - 9$

Answer

We have
$x^{2} - y^{2} + 6 y - 9$
$= x^{2} - (y^{2} - 6 y + 9)$
$= x^{2} - (y^{2} - 2 \times y \times 3 + 3^{2})$
$= x^{2} - {(y - 3)}^{2}$
$= {x + (y - 3)} {x - (y - 3)}$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (x + y - 3) (x - y + 3)$ .

The question number 32 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

32. $4 x^{2} - 9 y^{2} - 2 x - 3 y$

Answer

We have
$4 x^{2} - 9 y^{2} - 2 x - 3 y$
$= (4 x^{2} - 9 y^{2}) - (2 x + 3 y)$
$= {{(2 x)}^{2} - {(3 y)}^{2}} - (2 x + 3 y)$
$= {(2 x + 3 y) (2 x - 3 y)} - (2 x + 3 y)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (2 x + 3 y) {(2 x - 3 y) - 1}$
$= (2 x + 3 y) (2 x - 3 y - 1)$

The question number 33 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

33. $9 a^{2} + 3 a - 8 b - 64 b^{2}$

Answer

We have
$9 a^{2} + 3 a - 8 b - 64 b^{2}$
$= 9 a^{2} - 64 b^{2} + 3 a - 8 b$
$= (9 a^{2} - 64 b^{2}) + (3 a - 8 b)$
$= [{(3 a)}^{2} - {(8 b)}^{2}] + (3 a - 8 b)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= [(3 a + 8 b) (3 a - 8 b)] + (3 a - 8 b)$
$= (3 a - 8 b) [(3 a + 8 b) + 1]$
$= (3 a - 8 b) (3 a + 8 b + 1)$ .

The question number 34 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

34. $x^{2} + \frac{1}{x^{2}} - 3$

Answer

We have
$x^{2} + \frac{1}{x^{2}} - 3$
$= x^{2} + \frac{1}{x^{2}} - 2 - 1$
$= (x^{2} + \frac{1}{x^{2}} - 2) - 1$
$= {(x - \frac{1}{x})}^{2} - 1^{2}$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (x - \frac{1}{x} + 1) (x - \frac{1}{x} - 1)$ .

The question number 35 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

35. $x^{2} - 2 + \frac{1}{x^{2}} - y^{2}$

Answer

We have
$x^{2} - 2 + \frac{1}{x^{2}} - y^{2}$
$= (x^{2} - 2 + \frac{1}{x^{2}}) - y^{2}$
$= (x^{2} - 2 \times x \times \frac{1}{x} + \frac{1}{x^{2}}) - y^{2}$
$= {(x - \frac{1}{x})}^{2} - y^{2}$
$= (x - \frac{1}{x} - y) (x - \frac{1}{x} + y)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

The question number 36 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

36. $x^{4} + \frac{4}{x^{4}}$

Answer

We have
$x^{4} + \frac{4}{x^{4}}$
$= x^{4} + \frac{4}{x^{4}} + 4 - 4$
$= (x^{4} + \frac{4}{x^{4}} + 4) - 4$
$= [{(x^{2})}^{2} + {(\frac{2}{x^{2}})}^{2} + 2 \times x^{2} \times \frac{2}{x^{2}}] - 2^{2}$
$= {(x^{2} + \frac{2}{x^{2}})}^{2} - 2^{2}$
$= (x^{2} + \frac{2}{x^{2}} + 2) (x^{2} + \frac{2}{x^{2}} - 2)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

The question number 37 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

37. $x^{8} - 1$

Answer

We have
$x^{8} - 1$

$= {(x^{4})}^{2} - 1^{2}$

$= (x^{4} + 1) (x^{4} - 1)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

$= (x^{4} + 1) {{(x^{2})}^{2} - 1^{2}}$

$= (x^{4} + 1) (x^{2} + 1) (x^{2} - 1)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

$= (x^{4} + 1) (x^{2} + 1) (x^{2} - 1^{2})$

$= (x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

Now, we will factorise $(x^{4} + 1)$ .

$= (x^{4} + 1 + 2 x^{2} - 2 x^{2}) (x^{2} + 1) (x + 1) (x - 1)$

$= [{x^{4} + 1 + 2 x^{2}} - 2 x^{2}] (x^{2} + 1) (x + 1) (x - 1)$

$= [{{(x^{2})}^{2} + 1^{2} + 2 \times x^{2} \times 1} - {(\sqrt{2} x)}^{2}] (x^{2} + 1) (x + 1) (x - 1)$

Using ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$

$= [{(x^{2} + 1)}^{2} - {(\sqrt{2} x)}^{2}] (x^{2} + 1) (x + 1) (x - 1)$

Using $(a^{2} - b^{2}) = (a - b) (a + b)$

$= (x^{2} + 1 + \sqrt{2} x) (x^{2} + 1 - \sqrt{2} x) (x^{2} + 1) (x + 1) (x - 1)$

The question number 38 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

38. $16 x^{4} - 1$

Answer

We have
$16 x^{4} - 1$

$= {(4 x^{2})}^{2} - 1^{2}$

$= (4 x^{2} + 1) (4 x^{2} - 1)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

$= (4 x^{2} + 1) [{(2 x)}^{2} - 1^{2}]$

$= (4 x^{2} + 1) (2 x - 1) (2 x + 1)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

The question number 39 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

39. $81 x^{4} - y^{4}$

Answer

We have
$81 x^{4} - y^{4}$

$= {(9 x^{2})}^{2} - {(y^{2})}^{2}$

$= (9 x^{2} + y^{2}) (9 x^{2} - y^{2})$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

$= (9 x^{2} + y^{2}) [{(3 x)}^{2} - {(y)}^{2}]$

$= (9 x^{2} + y^{2}) (3 x + y) (3 x - y)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

The question number 40 of Exercise 3B RS Aggarwal Class 9 asks us to factorise the given algebraic expression.

40. $x^{4} - 625$

Answer

We have
$x^{4} - 625$

$= {(x^{2})}^{2} - {(25)}^{2}$

$= (x^{2} + 25) (x^{2} - 25)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

$= (x^{2} + 25) (x^{2} - 5^{2})$

$= (x^{2} + 25) (x + 5) (x - 5)$ ... $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

Related Links 🔗

Exercise 3B RS Aggarwal Class 9 Mathematics Solutions

Factorise:

1. 9x2−16y2

Answer

2. (254x2−19y2)

Answer

3. 81−16x2

Answer

4. 5−20x2

Answer

5. 2x4−32

Answer

6. 3a3b−243ab3

Answer

7. 3x3−48x

Answer

8. 27a2−48b2

Answer

9. x−64x3

Answer

10. 8ab2−18a3

Answer

11. 150−6x2

Answer

12. 2−50x2

Answer

13. 20x2−45

Answer

14. (3a+5b)2−4c2

Answer

15. a2−b2−a−b

Answer

16. 4a2−9b2−2a−3b

Answer

17. a2−b2+2bc−c2

Answer

18. 4a2−4b2+4a+1

Answer

19. a2+2ab+b2−9c2

Answer

20. 108a2−3(b−c)2

Answer

21. (a+b)3−a−b

Answer

22. x2+y2−z2−2xy

Answer

23. x2+2xy+y2−a2+2ab−b2

Answer

24. 25x2−10x+1−36y2

Answer

25. a−b−a2+b2

Answer

26. a2−b2−4ac+4c2

Answer

27. 9−a2+2ab−b2

Answer

28. x3−5x2−x+5

Answer

29. 1+2ab−(a2+b2)

Answer

30. 9a2+6a+1−36b2

Answer

31. x2−y2+6y−9

Answer

32. 4x2−9y2−2x−3y

Answer

33. 9a2+3a−8b−64b2

Answer

34. x2+1x2−3

Answer

35. x2−2+1x2−y2

Answer

36. x4+4x4

Answer

37. x8−1

Answer

38. 16x4−1

Answer

39. 81x4−y4

1. $9 x^{2} - 16 y^{2}$

2. $(\frac{25}{4} x^{2} - \frac{1}{9} y^{2})$

3. $81 - 16 x^{2}$

4. $5 - 20 x^{2}$

5. $2 x^{4} - 32$

6. $3 a^{3} b - 243 a b^{3}$

7. $3 x^{3} - 48 x$

8. $27 a^{2} - 48 b^{2}$

9. $x - 64 x^{3}$

10. $8 a b^{2} - 18 a^{3}$

11. $150 - 6 x^{2}$

12. $2 - 50 x^{2}$

13. $20 x^{2} - 45$

14. ${(3 a + 5 b)}^{2} - 4 c^{2}$

15. $a^{2} - b^{2} - a - b$

16. $4 a^{2} - 9 b^{2} - 2 a - 3 b$

17. $a^{2} - b^{2} + 2 b c - c^{2}$

18. $4 a^{2} - 4 b^{2} + 4 a + 1$

19. $a^{2} + 2 a b + b^{2} - 9 c^{2}$

20. $108 a^{2} - 3 {(b - c)}^{2}$

21. ${(a + b)}^{3} - a - b$

22. $x^{2} + y^{2} - z^{2} - 2 x y$

23. $x^{2} + 2 x y + y^{2} - a^{2} + 2 a b - b^{2}$

24. $25 x^{2} - 10 x + 1 - 36 y^{2}$

25. $a - b - a^{2} + b^{2}$

26. $a^{2} - b^{2} - 4 a c + 4 c^{2}$

27. $9 - a^{2} + 2 a b - b^{2}$

28. $x^{3} - 5 x^{2} - x + 5$

29. $1 + 2 a b - (a^{2} + b^{2})$

30. $9 a^{2} + 6 a + 1 - 36 b^{2}$

31. $x^{2} - y^{2} + 6 y - 9$

32. $4 x^{2} - 9 y^{2} - 2 x - 3 y$

33. $9 a^{2} + 3 a - 8 b - 64 b^{2}$

34. $x^{2} + \frac{1}{x^{2}} - 3$

35. $x^{2} - 2 + \frac{1}{x^{2}} - y^{2}$

36. $x^{4} + \frac{4}{x^{4}}$

37. $x^{8} - 1$

38. $16 x^{4} - 1$

39. $81 x^{4} - y^{4}$

40. $x^{4} - 625$