Question
Answer
$$(6-x)(3-x)^2=-x^3+12x^2-45x+54$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6-x)(3-x)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6-x)(9-6x+x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}54-36x+6x^2-9x+6x^2-x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-x^3+12x^2-45x+54\end{aligned} $$ | |
| ① | Find $ \left(3-x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3 } $ and $ B = \color{red}{ x }$. $$ \begin{aligned}\left(3-x\right)^2 = \color{blue}{3^2} -2 \cdot 3 \cdot x + \color{red}{x^2} = 9-6x+x^2\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{6-x}\right) $ by each term in $ \left( 9-6x+x^2\right) $. $$ \left( \color{blue}{6-x}\right) \cdot \left( 9-6x+x^2\right) = 54-36x+6x^2-9x+6x^2-x^3 $$ |
| ③ | Combine like terms: $$ 54 \color{blue}{-36x} + \color{red}{6x^2} \color{blue}{-9x} + \color{red}{6x^2} -x^3 = -x^3+ \color{red}{12x^2} \color{blue}{-45x} +54 $$ |
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