Answer
$$(4-2x)^3=-8x^3+48x^2-96x+64$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4-2x)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}64-96x+48x^2-8x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-8x^3+48x^2-96x+64\end{aligned} $$ | |
| ① | Find $ \left(4-2x\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 4 $ and $ B = 2x $. $$ \left(4-2x\right)^3 = 4^3-3 \cdot 4^2 \cdot 2x + 3 \cdot 4 \cdot \left( 2x \right)^2-\left( 2x \right)^3 = 64-96x+48x^2-8x^3 $$ |
| ② | Combine like terms: $$ -8x^3+48x^2-96x+64 = -8x^3+48x^2-96x+64 $$ |
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