Question

Find x cube +y cube -12xy+64

When x+y= -4

Answer 1

$x + y = - 4 \\ cubing \: on \: both \: sides \\ {(x + y)}^{3} = - 64 \\ {(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ba(a + b) \\ {x}^{3} + {y}^{3} + 3xy(x + y) = { - 4}^{3} \\ \\ {x}^{3} + {y}^{3} + 3xy( - 4) = - 64 \\ {x}^{3} + {y}^{3} - 12xy + 64 = 0$