Question
Answer
$$(3u-6+4u^2-8u+4v^2)^2=16u^4+32u^2v^2+16v^4-40u^3-40uv^2-23u^2-48v^2+60u+36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3u-6+4u^2-8u+4v^2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4u^2+4v^2-5u-6)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}16u^4+32u^2v^2+16v^4-40u^3-40uv^2-23u^2-48v^2+60u+36\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{3u} -6+4u^2 \color{blue}{-8u} +4v^2 = 4u^2+4v^2 \color{blue}{-5u} -6 $$ |
| ② | Multiply each term of $ \left( \color{blue}{4u^2+4v^2-5u-6}\right) $ by each term in $ \left( 4u^2+4v^2-5u-6\right) $. $$ \left( \color{blue}{4u^2+4v^2-5u-6}\right) \cdot \left( 4u^2+4v^2-5u-6\right) = \\ = 16u^4+16u^2v^2-20u^3-24u^2+16u^2v^2+16v^4-20uv^2-24v^2-20u^3-20uv^2+25u^2+30u-24u^2-24v^2+30u+36 $$ |
| ③ | Combine like terms: $$ 16u^4+ \color{blue}{16u^2v^2} \color{red}{-20u^3} \color{green}{-24u^2} + \color{blue}{16u^2v^2} +16v^4 \color{orange}{-20uv^2} \color{blue}{-24v^2} \color{red}{-20u^3} \color{orange}{-20uv^2} + \color{red}{25u^2} + \color{green}{30u} \color{red}{-24u^2} \color{blue}{-24v^2} + \color{green}{30u} +36 = \\ = 16u^4+ \color{blue}{32u^2v^2} +16v^4 \color{red}{-40u^3} \color{orange}{-40uv^2} \color{red}{-23u^2} \color{blue}{-48v^2} + \color{green}{60u} +36 $$ |
This page was created using
Simplify polynomials calculator