Simplify $(2 x y^{2} - x^{2} y^{2}) (3 x + y - 4 x y)$ and find the product when $x = - 2 and y = - 1$

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Solution

$(2 x y^{2} - x^{2} y^{2}) (3 x + y - 4 x y)$
$6 x^{2} y^{2} + 2 x y^{3} - 8 x^{2} y^{3} - 3 x^{3} y^{2} - x^{2} y^{3} + 4 x^{3} y^{3}$
$6 x^{2} y^{2} + 2 x y^{3} - 9 x^{2} y^{3} - 3 x^{3} y^{2} + 4 x^{3} y^{3}$
when $x = - 2$ and $y = - 1$
$= 6 (- 2)^{2} (- 1)^{2} + 2 (- 2) (- 1)^{3} - 9 (- 2)^{2} (- 1)^{3} - 3 (- 2)^{3} (- 1)^{2} + 4 (- 2)^{3} (- 1)^{3}$
$= 6 (4) + 4 - 9 (- 4) - 3 (- 8) + 4 (8)$
$= 24 + 4 + 36 + 24 + 32$
$= 120$

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