Question
Answer
$$(4y-2z^2)^3=-8z^6+48yz^4-96y^2z^2+64y^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4y-2z^2)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}64y^3-96y^2z^2+48yz^4-8z^6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-8z^6+48yz^4-96y^2z^2+64y^3\end{aligned} $$ | |
| ① | Find $ \left(4y-2z^2\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 4y $ and $ B = 2z^2 $. $$ \left(4y-2z^2\right)^3 = \left( 4y \right)^3-3 \cdot \left( 4y \right)^2 \cdot 2z^2 + 3 \cdot 4y \cdot \left( 2z^2 \right)^2-\left( 2z^2 \right)^3 = 64y^3-96y^2z^2+48yz^4-8z^6 $$ |
| ② | Combine like terms: $$ -8z^6+48yz^4-96y^2z^2+64y^3 = -8z^6+48yz^4-96y^2z^2+64y^3 $$ |
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