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RD Chapter 5 Factorisation of Algebraic Expressions Ex 5.2 Solutions

Question - 11 : - 8x2y3 – x5

Answer - 11 : -

8x2y3 – x5 = x2(8y3 –X3)
= x2(2y)3 – (x)3]
= x2[(2y – x) (2y)2 + 2y x x + (x)2]
= x2(2y – x) (4y2 + 2xy + x2)

Question - 12 : - 1029 -3x3

Answer - 12 : -

1029 – 3X3 = 3(343 – x3)                      ‘
= 3 [(7)3 – (x)3]
= 3(7 – x) (49x + 7x + x2)

Question - 13 : - x3y3+ 1

Answer - 13 : -

x3y3 + 1 = (xy)3 +(1)3
= (xy + 1) [(xy)2 – xy x 1 + (1)2]
= (xy + 1) (x2y2 – xy + 1)
= (xy + 1) (x2y – xy + 1)

Question - 14 : - x4y4 – xy

Answer - 14 : -

x4y4 – xy = xy(x3y3 –1)
= xy[(xy3-(1)3]
= xy (xy – 1) [x2y2 + 2xy + 1]

Question - 15 : - a3 + b3 + a + b

Answer - 15 : -

a3 + b3 + a + b
= (a + b) (a2 – ab + b2) + 1 (a + b)
= (a + b) (a2 – ab + b2 + 1)

Question - 16 : - Simplify:

Answer - 16 : -


Question - 17 : - (a + b)3 – 8(a – b)3

Answer - 17 : -

(a + b)3 – 8(a – b)3
= (a + b)2 – (2a – 2b)3
= (a+ b – 2a + 2b) [(a + b)2 + (a + b) (2a-2b) + (2a –2b)2)]
= (3b – a) [a2 + b2 + 2ab + 2a2 – 2ab+ 2ab – 2b2 + 4a2 – 8ab + 4b2]
= (3b – a) [7a2 – 6ab + 3b2]

Question - 18 : - (x + 2)3 + (x- 2)3

Answer - 18 : -

(x + 2)3 + (x – 2)3
= (x + 2 + x – 2) [(x + 2)2 – (x + 2) (x – 2) + (x – 2)2]
= 2x [x2 + 4x + 4 – (x2 + 2x – 2x – 4) + x2 4x+ 4]
= 2x[x2 + 4x + 4- x2-2x + 2x + 4+ x2– 4x+ 4]
= 2x[x2 + 12]

Question - 19 : - x6 +y6

Answer - 19 : -

x6 + y6 = (x2)3 +(y2)3
= (x2 + y2) [x4 – x2y2 +y4]

Question - 20 : - a12 + b12

Answer - 20 : -

a12 + b12 = (a4)3 +(b4)3
= (a4 + b4) [(a4)2 –a4b4 + (b4)2]
= (a4 + b4) (a8 – a4b4 +b8)

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