Question
Answer
$$(v+h)^2+4(hv-2)=h^2+6hv+v^2-8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(v+h)^2+4(hv-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}v^2+2hv+h^2+4(hv-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}v^2+2hv+h^2+4hv-8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}h^2+6hv+v^2-8\end{aligned} $$ | |
| ① | Find $ \left(v+h\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ v } $ and $ B = \color{red}{ h }$. $$ \begin{aligned}\left(v+h\right)^2 = \color{blue}{v^2} +2 \cdot v \cdot h + \color{red}{h^2} = v^2+2hv+h^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{4} $ by $ \left( hv-2\right) $ $$ \color{blue}{4} \cdot \left( hv-2\right) = 4hv-8 $$ |
| ③ | Combine like terms: $$ v^2+ \color{blue}{2hv} +h^2+ \color{blue}{4hv} -8 = h^2+ \color{blue}{6hv} +v^2-8 $$ |
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