Answer
$$y(4-4y)^3=-64y^4+192y^3-192y^2+64y$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}y(4-4y)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}y(64-192y+192y^2-64y^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}64y-192y^2+192y^3-64y^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-64y^4+192y^3-192y^2+64y\end{aligned} $$ | |
| ① | Find $ \left(4-4y\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 4 $ and $ B = 4y $. $$ \left(4-4y\right)^3 = 4^3-3 \cdot 4^2 \cdot 4y + 3 \cdot 4 \cdot \left( 4y \right)^2-\left( 4y \right)^3 = 64-192y+192y^2-64y^3 $$ |
| ② | Multiply $ \color{blue}{y} $ by $ \left( 64-192y+192y^2-64y^3\right) $ $$ \color{blue}{y} \cdot \left( 64-192y+192y^2-64y^3\right) = 64y-192y^2+192y^3-64y^4 $$ |
| ③ | Combine like terms: $$ -64y^4+192y^3-192y^2+64y = -64y^4+192y^3-192y^2+64y $$ |
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