Question

X-y=2 then find x^3-y^3-6xy

Answer 1

expand (x-y)^3 = 2^3
which causes
x^3-y^3-3xy(x-y) = 8
x^3-y^3-6xy = 8

Answer 2

$x - y = 2 \\ {x}^{3} - {y}^{3} - 6xy \\ = (x - y)( {x}^{2} + {y}^{2} + xy) - 6xy \\ = 2( {x }^{2} + {y}^{2} + xy) - 6xy \\ = 2 {x}^{2} + 2 {y}^{2} - 4xy \\ =2( {x}^{2} + {y}^{2} - 2xy) \\ = 2 {(x - y)}^{2} \\ = 2 \times {2}^{2} \\ = 8$