Question

If x + y + 4 = 0, find the value of (x³ + y³ − 12xy + 64).

Answer 1

$$\begin{gathered} x^3+y^3-12xy+64 \\ =x^3+y^3+64-12xy \\ =x^3+y^3+4^3-3\times x\times y\times 4 \\ =\left(x+y+4\right)\left(x^2+y^2+4^2-xy-4y-4x\right) \\ =0\times \left(x^2+y^2+16-xy-4y-4x\right)\left(\mathrm{Given}:\mathrm{x\; +\; y\; +\; 4\; =\; 0}\right) \\ =0 \end{gathered}$$