Answer
$$(9-x^2)^3=-x^6+27x^4-243x^2+729$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(9-x^2)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}729-243x^2+27x^4-x^6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-x^6+27x^4-243x^2+729\end{aligned} $$ | |
| ① | Find $ \left(9-x^2\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 9 $ and $ B = x^2 $. $$ \left(9-x^2\right)^3 = 9^3-3 \cdot 9^2 \cdot x^2 + 3 \cdot 9 \cdot \left( x^2 \right)^2-\left( x^2 \right)^3 = 729-243x^2+27x^4-x^6 $$ |
| ② | Combine like terms: $$ -x^6+27x^4-243x^2+729 = -x^6+27x^4-243x^2+729 $$ |
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