Answer
$$(4x^2-2x^7)^2=4x^{14}-16x^9+16x^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4x^2-2x^7)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}16x^4-16x^9+4x^{14} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^{14}-16x^9+16x^4\end{aligned} $$ | |
| ① | Find $ \left(4x^2-2x^7\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^2 } $ and $ B = \color{red}{ 2x^7 }$. $$ \begin{aligned}\left(4x^2-2x^7\right)^2 = \color{blue}{\left( 4x^2 \right)^2} -2 \cdot 4x^2 \cdot 2x^7 + \color{red}{\left( 2x^7 \right)^2} = 16x^4-16x^9+4x^{14}\end{aligned} $$ |
| ② | Combine like terms: $$ 4x^{14}-16x^9+16x^4 = 4x^{14}-16x^9+16x^4 $$ |
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