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:
RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2E 34

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

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