RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2F

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2F.

Other Exercises

Factorize :

Question 1.
Solution:
25x2 – 64y2
= (5x)2 – (8y)2
= (5x + 8y) (5x – 8y) Ans.

Question 2.
Solution:
100 – 9x2
(10)2 – (3x)2
= (10 + 3x) (10 – 3x) Ans.

Question 3.
Solution:
5x2 – 7y2
=(√5x)2 +(√7y)2
=(√5x – √7y)(√5x – √7y) Ans

Question 4.
Solution:
(3x + 5y)2 – 4z2
= (3x + 5y)2 – (2z)2
= (3x + 5y + 2z) (3x + 5y – 2z) Ans.

Question 5.
Solution:
150 – 6x2
= 6(25 – x2)
= 6{(5)2 – (x2)}
= 6 (5 + x) (5 – x) Ans.

Question 6.
Solution:
20x2 – 45
= 5 (4x2 – 9)
= 5{(2x)2 – (3)2}
= 5 (2x + 3) (2x – 3) Ans.

Question 7.
Solution:
3x3 – 48x
= 3x (x2 – 16)
= 3x {(x)2 – (4)2}
= 3x (x + 4) (x – 4) Ans.

Question 8.
Solution:
2 – 50x2
= 2(1 – 25x2) = 2 {(1)2 – (5x)2}
= 2 (1 + 5x) (1 – 5x) Ans.

Question 9.
Solution:
27a2 – 48b2
= 3(9a2 – 16b2)
= 3 {(3a)2 – (4b)2}
= 3(3a + 4b) (3a – 4b) Ans.

Question 10.
Solution:
x – 64x3
= x (1 – 64x2)
= x{(1)2 – (8x)2}
= x (1 + 8x) (1 – 8x) Ans.

Question 11.
Solution:
8ab2 – 18a3
= 2a (4b2 – 9a2)
= 2a {(2b)2 – (3a)2}
= 2a (2b + 3a) (2b – 3a) Ans

Question 12.
Solution:
3a3b – 243ab3
= 2ab (a2 -81 b2)
= 3ab {(a)2 – (9b)2}
= 3ab (a + 9b) (a – 9b) Ans.

Question 13.
Solution:
(a + b)3 – a – b
= (a + b)3 – 1 (a + b)
= (a + b) {(a + b)2 – 1}
= (a + b) {(a + b)2 – (1)2}
= (a + b) (a + b + 1) (a + b – 1) Ans.

Question 14.
Solution:
108 a2 – 3(b – c)2
= 3 {36a2 – (b – c)2}
= 3 {(6a)2 – (b – c)2}
= 3 {(6a + (b – c)} {6a – (b – c)}
= 3 (6a + b – c) (6a – b + c) Ans.

Question 15.
Solution:
x3 – 5x2 – x + 5
= x2(x – 5) -1(x – 5)
= (x – 5) (x2 – 1)
= (x – 5) {(x)2 – (1)2}
= (x – 5) (x + 1) (x – 1) Ans.

Question 16.
Solution:
a2 + 2ab + b2 – 9c2
= (a + b)2 – (3c)2
= {a2 + b2 + 2ab – (a + b)2}
= (a + b + 3c) (a + b – 3c) Ans.

Question 17.
Solution:
9 – a2 + 2ab – b2
= 9 – (a2 – 2ab + b2)
= (3)2 -(a- b)2
{ ∴a2 + b2 – 2ab = (a – b)2}
= (3 + a – b) (3 – a + b) Ans.

Question 18.
Solution:
a2 – b2 – 4ac + 4c2
= a2 – 4ac + 4c2 – b2
= (a)2 – 2 x a x 2c + (2c)2 – (b)2
= (a – 2c)2 – (b)2
= (a – 2c + b) (a – 2c – b)
= (a + b – 2c) (a – b – 2c) Ans.

Question 19.
Solution:
9a2 + 3a – 8B – 64b2
= 9a2 – 64b2 + 3a – 8b
= (3a)2 – (8b)2 + 1(3a – 8b)
= (3a + 8b) (3a – 8b) + 1 (3a – 8b)
= (3a – 8b) (3a + 8b + 1) Ans.

Question 20.
Solution:
x2 – y2 + 6y _ 9
= (x)2 – (y2 – 6y + 9)
= (x)2 – {(y)2 – 2 x y x 3 + (3)2}
= (x)2 – (y – 3)2
= (x + y – 3) (x – y + 3) Ans.

Question 21.
Solution:
4x2 – 9y2 – 2x – 3y
= (2x)2 – (3y)2 – 1(2x + 3y)
= (2x + 3y) (2x – 3y) – 1( 2x + 3y)
= (2x + 3y) (2x – 3y – 1) Ans.

Question 22.
Solution:
x4 – 1
= (x2)2 – (1)2
= (x2 + 1) (x2 – 1)
= (x2 + 1) {(x)2 – (1)2}
= (x2 + 1) (x + 1) (x – 1) Ans.

Question 23.
Solution:
a – b – a2+ b2
= 1 (a – b) – (a2 – b2)
= 1 (a – b) – (a + b) (a – b)
= (a – b) (1 – a – b) Ans.

Question 24.
Solution:
x4 – 625
= (x2)2 – (25)2
= (x2 + 25) (x2 – 25)
= (x2 + 25) {(x)2 – (5)2}
= (x2 + 25) (x + 5) (x – 5) Ans.

Hope given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2F are helpful to complete your math homework.

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