Answer
$$(x+y)(2xy+y-2x-3)=2x^2y+2xy^2-2x^2-xy+y^2-3x-3y$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+y)(2xy+y-2x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^2y+2xy^2-2x^2-xy+y^2-3x-3y\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+y}\right) $ by each term in $ \left( 2xy+y-2x-3\right) $. $$ \left( \color{blue}{x+y}\right) \cdot \left( 2xy+y-2x-3\right) = 2x^2y+xy-2x^2-3x+2xy^2+y^2-2xy-3y $$ |
| ② | Combine like terms: $$ 2x^2y+ \color{blue}{xy} -2x^2-3x+2xy^2+y^2 \color{blue}{-2xy} -3y = 2x^2y+2xy^2-2x^2 \color{blue}{-xy} +y^2-3x-3y $$ |
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