Question

Factorize:
x³ + y³ − 12xy + 64

Answer 1

$$\begin{gathered} x^3+y^3-12xy+64=x^3+y^3+64-12xy \\ =x^3+y^3+4^3-3\times x\times y\times 4 \\ =\left(x+y+4\right)\left(x^2+y^2+4^2-xy-4y-4x\right) \\ =\left(x+y+4\right)\left(x^2+y^2+16-xy-4y-4x\right) \end{gathered}$$