Question

Using the identity
${a}^{3} + {b}^{3} + {c}^{3} - 3abc = ( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac)(a + b + c)$
multiply
$9 {x}^{2} + 25 {y}^{2} + 15xy + 12x - 20y + 16$
by
$3x - 5y - 4$

Answer 1

$( {9x}^{2} + 25 {y}^{2} + 15xy + 12x - 20y + 16) \times (3x - 5y - 4) \\ ( {3x)}^{2}$
${{(3x)}^{2} + {( - 5y)}^{2} + {( - 4)}^{2} - (3x)( - 5y) - (3x)( - 4) - ( - 5y)( - 4)}{3x + ( - 5y) + ( - 4)} \\ {(3x)}^{3} + {( - 5y)}^{3} + {( - 4)}^{3} - 3(3x)( - 5y)( - 4) \\ 27 {x}^{3} - 125 {y}^{3} - 64 - 180xy$