Answer
$$(4-r)(-(8-r)^2)=r^3-20r^2+128r-256$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4-r)(-(8-r)^2)& \xlongequal{ }(4-r)(-(64-16r+r^2)) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4-r)(-64+16r-r^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-256+64r-4r^2+64r-16r^2+r^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}r^3-20r^2+128r-256\end{aligned} $$ | |
| ① | Remove the parentheses by changing the sign of each term within them. $$ - \left(64-16r+r^2 \right) = -64+16r-r^2 $$ |
| ② | Multiply each term of $ \left( \color{blue}{4-r}\right) $ by each term in $ \left( -64+16r-r^2\right) $. $$ \left( \color{blue}{4-r}\right) \cdot \left( -64+16r-r^2\right) = -256+64r-4r^2+64r-16r^2+r^3 $$ |
| ③ | Combine like terms: $$ -256+ \color{blue}{64r} \color{red}{-4r^2} + \color{blue}{64r} \color{red}{-16r^2} +r^3 = r^3 \color{red}{-20r^2} + \color{blue}{128r} -256 $$ |
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