## RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2E

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

Other Exercises

Factorize:

Question 1.
Solution:
9x2 + 12xy
= 3x (3x + 4y) Ans.

Question 2.
Solution:
18x2y – 24xyz
= 6xy (3x – 4z) Ans.

Question 3.
Solution:
27a3b3 – 45a4b2
= 9a3b2 (3b – 5a) Ans.

Question 4.
Solution:
2a (x + y) – 3b(x + y)
= (x + y) (2a – 3b) Ans.

Question 5.
Solution:
2x (p2 + q2) + 4y (p2 + q2)
= 2(p2 + q2) (x + 2y) Ans

Question 6.
Solution:
x (a – 5) + y (5 – a)
= x (a – 5) -y (a – 5)
= (a – 5) (x – y) Ans.

Question 7.
Solution:
4(a + b) – 6 (a + b)2
= 2(a + b) {2 – 3 (a + b)}
= 2(a + b) (2 – 3a – 3b) Ans.

Question 8.
Solution:
8(3a – 2b)2 – 10 (3a – 2b)
= 2(3a – 2b) {4 (3a – 2b) – 5}
= 2(3a – 2b) (12a – 8b – 5) Ans.

Question 9.
Solution:
x (x + x)3 – 3x2 y (x + y)
= x (x + y) {(x + y)2 – 3xy}
= x (x + y) [x2 + y2 + 2xy – 3xy)
= x (x + y) (x2 + y2 – xy) Ans.

Question 10.
Solution:
x3 + 2x2 + 5x + 10
= x2 (x + 2) + 5 (x + 2)
= (x + 2) (x2 + 5) Ans.

Question 11.
Solution:
x2 + xy – 2xz – 2yz
= x (x + y) -2z (x + y)
= (x + y) (x – 2z) Ans.

Question 12.
Solution:
a3 b – a2b + 5ab – 5b.
= b (a3 – a2 + 5a – 5)
= b {(a2 (a – 1) + 5 (a – 1)}
= b (a – 1) (a2 + 5) Ans.

Question 13.
Solution:
8 – 4a – 2a3 + a4
= 4 (2 – a) – a3 (2 – a)
= (2 – a) (4 – a3) Ans.

Question 14.
Solution:
x3 – 2x2y + 3xy2 – 6y3
= x2 (x – 2y) + 3y2 (x – 2y)
= (x – 2y) (x2 + 3y2) Ans

Question 15.
Solution:
px – 5q + pq – 5x
= px – 5x + pq – 5q
= x(p – 5) + q(p – 5)
= {p – 5) (x + q) Ans.

Question 16.
Solution:
x2 + y – xy – x
= x2 – x – xy + y
= x (x – 1) – y (x – 1)
= (x – 1) (x – y) Ans.

Question 17.
Solution:
(3a – 1)2 – 6a + 2
= (3a – 1)2 – 2 (3a – 1)
= (3a – 1) (3a – 1 – 2)
= (3a – 1) (3a – 3)
= 3(3a – 1) (a – 1) Ans.

Question 18.
Solution:
(2x – 3)2 – 8x + 12
= (2x – 3)2 – 4(2x – 3)
= (2x – 3) (2x – 3 – 4)
= (2x – 3) (2x – 7) Ans.

Question 19.
Solution:
a3 + a – 3a2 – 3
= a3 – 3a2 + a – 3
= a2 (a – 3) + 1 (a – 3)
= (a – 3) (a2 + 1) Ans.

Question 20.
Solution:
3ax – 6ay – 8by + 4bx
= 3ax – 6ay + 4bx – 8by
= 3a (x – 2y) + 4b (x – 2y)
= (x – 2y) (3a + 4b) Ans

Question 21.
Solution:
abx2 + a2x + b2x + ab
= ax (bx + a) + b (bx + a)
= (bx + a) (ax + b) Ans.

Question 22.
Solution:
x3 – x2 + ax + x – a – 1
= x3 – x2 + ax – a + x – 1
= x2 (x – 1) + a (x – 1) + 1 (x – 1)
= (x – 1) (x2 + a + 1) Ans.

Question 23.
Solution:
2x + 4y – 8xy – 1
= 2x – 8xy -1+4y
= 2x (1 – 4y) -1 (1 – 4y)
= (1 – 4y) (2x – 1) Ans.

Question 24.
Solution:
ab (x2 +y2) – xy (a2 + b2)
= abx2 + aby2 – a2xy – b2xy
= abx2 – a2xy – b2xy + aby2
= ax (bx – ay) – by (bx – ay)
= (bx – ay) (ax – by) Ans.

Question 25.
Solution:
a2 + ab (b + 1) + b3
= a2 + ab2 + ab + b3
= a (a + b2) + b (a + b2)
= (a + b2) (a + b) Ans

Question 26.
Solution:
a3 + ab (1 – 2a) – 2b2
= a3 + ab – 2a2b – 2b2
= a3 – 2a2b + ab – 2b2
= a2 (a – 2b) + b (a – 2b)
= (a – 2b) (a2 + b) Ans.

Question 27.
Solution:
2a2 + bc – 2ab – ac
= 2a2 – 2ab – ac + bc
= 2a (a – b) – c (a – b)
= (a – b) (2a – c) Ans.

Question 28.
Solution:
(ax + by)2 + (bx – ay)2
= a2x2 + b2y2 + 2abxy + b2x2 + a2y2 – 2bxy
= a2x2 + b2y2 + b2x2 + a2y2
= a2x2 + b2x2 + a2y2 + b2y2
= x2(a2 + b2) + y2(a2 + b2)
= (a2 + b2) (x2 + y2) Ans.

Question 29.
Solution:
a (a + b – c) – bc
= a2 + ab – ac – bc
= a (a + b) – c (a + b)
(a + b) (a – c) Ans.

Question 30.
Solution:
a(a – 2b – c) + 2bc
= a2 – 2ab – ac +2bc
= a2 – ac – 2ab + 2bc
= a (a – c) – 2b (a – c)
= (a – c) (a – 2b) Ans.

Question 31.
Solution:
a2x2 + (ax2 + 1) x + a
= a2x2 + ax3 + x + a
= a2x2 + ax3 + a + x
= ax2 (a + x) + 1 (a + x)
– (a + x) (ax2 + 1) Ans

Question 32.
Solution:
ab (x2 + 1) + x (a2 + b2)
= abx2 + ab + a2x + b2x
= abx2 + a2x + b2x + ab
= ax (bx + a) + b (bx + a)
= (bx + a) (ax + b) Ans.

Question 33.
Solution:
x2 – (a + b) x + ab
= x2 – ax – bx + ab
= x (x – a) – b (x – a)
= (x – a) (x – b) Ans.

Question 34.
Solution: Hope given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2E are helpful to complete your math homework.

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