Question
Answer
$$(x-372)(x+60)^2=x^3-252x^2-41040x-1339200$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-372)(x+60)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x-372)(x^2+120x+3600) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3+120x^2+3600x-372x^2-44640x-1339200 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-252x^2-41040x-1339200\end{aligned} $$ | |
| ① | Find $ \left(x+60\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 60 }$. $$ \begin{aligned}\left(x+60\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 60 + \color{red}{60^2} = x^2+120x+3600\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x-372}\right) $ by each term in $ \left( x^2+120x+3600\right) $. $$ \left( \color{blue}{x-372}\right) \cdot \left( x^2+120x+3600\right) = x^3+120x^2+3600x-372x^2-44640x-1339200 $$ |
| ③ | Combine like terms: $$ x^3+ \color{blue}{120x^2} + \color{red}{3600x} \color{blue}{-372x^2} \color{red}{-44640x} -1339200 = x^3 \color{blue}{-252x^2} \color{red}{-41040x} -1339200 $$ |
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