Question

Factorise: x3 + y3 + 12xy – 64​

Answer 1

x3 + y3 – 12xy + 64

⇒ x3 + y3 + 43 – 12xy

⇒ x3 + y3 + 43 - 3×4xy …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

x3 + y3 + 43 - 3×4xy = (x + y + 4) (x2 + y2 + 16 - xy - 4y - 4x)

(x + y + 4) (x2 + y2 + 16 - xy - 4y - 4x)

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