Question
Answer
$$(x^2+12x+32)(x+4)=x^3+16x^2+80x+128$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+12x+32)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3+4x^2+12x^2+48x+32x+128 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3+16x^2+80x+128\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+12x+32}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x^2+12x+32}\right) \cdot \left( x+4\right) = x^3+4x^2+12x^2+48x+32x+128 $$ |
| ② | Combine like terms: $$ x^3+ \color{blue}{4x^2} + \color{blue}{12x^2} + \color{red}{48x} + \color{red}{32x} +128 = x^3+ \color{blue}{16x^2} + \color{red}{80x} +128 $$ |
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