# Let us factorise

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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