Answer
$$(2-h)^3=-h^3+6h^2-12h+8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2-h)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8-12h+6h^2-h^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-h^3+6h^2-12h+8\end{aligned} $$ | |
| ① | Find $ \left(2-h\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 2 $ and $ B = h $. $$ \left(2-h\right)^3 = 2^3-3 \cdot 2^2 \cdot h + 3 \cdot 2 \cdot h^2-h^3 = 8-12h+6h^2-h^3 $$ |
| ② | Combine like terms: $$ -h^3+6h^2-12h+8 = -h^3+6h^2-12h+8 $$ |
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