Question

1+8x^(3)+18xy-27y^(3)​

Answer 1

1 + 8x^3 + 18xy – 27y^3

⇒ 13 + (2x)^ 3 + (- 3y) ^3 + 18xy

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

We use the identity

a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - 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 + 4x^2 + 9y^2 - 2x + 6xy + 3y)

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