Q4 of 65 Page 141

Let us factorise the following algebraic expressions:

1 + 8x3 + 18xy – 27y3

1 + 8x3 + 18xy – 27y3


⇒ 13 + (2x) 3 + (- 3y) 3 + 18xy


⇒ 13 + (2x) 3 + (- 3y) 3 + 3×(1)×(2x) (- 3y) …Equation(i)


We use the identity


a3 + b3 + c3 - 3abc = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)


Using the above identity in Equation (i) we get


⇒ 13 + (2x) 3 + (- 3y) 3 + 3×(1)×(2x) (- 3y) = (1 + 2x - 3y) (1 + 4x2 + 9y2 - 2x + 6xy + 3y)


(1 + 2x - 3y) (1 + 4x2 + 9y2 - 2x + 6xy + 3y)


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