Let us factorise the following algebraic expressions:

x³ + y³ – 12xy + 64

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)