Question
Answer
$$2(v^2-h^2)\cdot(1+v^2)=-2h^2v^2+2v^4-2h^2+2v^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(v^2-h^2)\cdot(1+v^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2v^2-2h^2)\cdot(1+v^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2v^2+2v^4-2h^2-2h^2v^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2h^2v^2+2v^4-2h^2+2v^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( v^2-h^2\right) $ $$ \color{blue}{2} \cdot \left( v^2-h^2\right) = 2v^2-2h^2 $$ |
| ② | Multiply each term of $ \left( \color{blue}{2v^2-2h^2}\right) $ by each term in $ \left( 1+v^2\right) $. $$ \left( \color{blue}{2v^2-2h^2}\right) \cdot \left( 1+v^2\right) = 2v^2+2v^4-2h^2-2h^2v^2 $$ |
| ③ | Combine like terms: $$ -2h^2v^2+2v^4-2h^2+2v^2 = -2h^2v^2+2v^4-2h^2+2v^2 $$ |
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