Answer
$$(4x-x^3)^2=x^6-8x^4+16x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4x-x^3)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}16x^2-8x^4+x^6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^6-8x^4+16x^2\end{aligned} $$ | |
| ① | Find $ \left(4x-x^3\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 4x } $ and $ B = \color{red}{ x^3 }$. $$ \begin{aligned}\left(4x-x^3\right)^2 = \color{blue}{\left( 4x \right)^2} -2 \cdot 4x \cdot x^3 + \color{red}{\left( x^3 \right)^2} = 16x^2-8x^4+x^6\end{aligned} $$ |
| ② | Combine like terms: $$ x^6-8x^4+16x^2 = x^6-8x^4+16x^2 $$ |
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