Answer
$$(x+2)(x+2)(x-3)=x^3+x^2-8x-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)(x+2)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x+2x+4)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+4x+4)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-3x^2+4x^2-12x+4x-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+x^2-8x-12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+2}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x+2}\right) \cdot \left( x+2\right) = x^2+2x+2x+4 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{2x} + \color{blue}{2x} +4 = x^2+ \color{blue}{4x} +4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+4x+4}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{x^2+4x+4}\right) \cdot \left( x-3\right) = x^3-3x^2+4x^2-12x+4x-12 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-3x^2} + \color{blue}{4x^2} \color{red}{-12x} + \color{red}{4x} -12 = x^3+ \color{blue}{x^2} \color{red}{-8x} -12 $$ |
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