Question
Answer
$$(4u-5v-2)(5u-4v+3)=20u^2-41uv+20v^2+2u-7v-6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4u-5v-2)(5u-4v+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}20u^2-41uv+20v^2+2u-7v-6\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4u-5v-2}\right) $ by each term in $ \left( 5u-4v+3\right) $. $$ \left( \color{blue}{4u-5v-2}\right) \cdot \left( 5u-4v+3\right) = 20u^2-16uv+12u-25uv+20v^2-15v-10u+8v-6 $$ |
| ② | Combine like terms: $$ 20u^2 \color{blue}{-16uv} + \color{red}{12u} \color{blue}{-25uv} +20v^2 \color{green}{-15v} \color{red}{-10u} + \color{green}{8v} -6 = \\ = 20u^2 \color{blue}{-41uv} +20v^2+ \color{red}{2u} \color{green}{-7v} -6 $$ |
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