Simplify the following expression and find the product when x = -2 and y = -1.   2xy2-x2y23x+y-4xy

# Simplify the following expression and find the product when x = -2 and y = -1.   $\left({2}{x}{{y}}^{{2}}{-}{{x}}^{{2}}{{y}}^{{2}}\right)\left({3}{x}{+}{y}{-}{4}{\mathit{xy}}\right)$

1. A
120
2. B
230
3. C
150
4. D
125

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### Solution:

${2}{\mathit{xy²}}{\left(}{3}{x}{+}{y}{-}{4}{\mathit{xy}}{\right)}{-}{\mathit{x²y²}}{\left(}{3}{x}{+}{y}{-}{4}{\mathit{xy}}{\right)}{.}$

${=}{6}{\mathit{x²y²}}{+}{2}{\mathit{xy³}}{-}{9}{\mathit{x²y³}}{-}{3}{\mathit{x³y³}}{+}{4}{\mathit{x³y³}}$

${6}{\left(}{-}{2}{\right)}{²}{\left(}{-}{1}{\right)}{²}{+}{2}{\left(}{-}{2}{\right)}{\left(}{-}{1}{\right)}{³}{-}{9}{\left(}{-}{2}{\right)}{²}{\left(}{-}{1}{\right)}{³}{-}{3}{\left(}{-}{2}{\right)}{³}{\left(}{-}{1}{\right)}{²}{+}{4}{\left(}{-}{2}{\right)}{³}{\left(}{-}{1}{\right)}{³}{.}$

${=}{24}{+}{4}{+}{36}{+}{24}{+}{32}$
${=}{120}$

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