Question
Answer
$$(x+3)(x-2)(x+1)(x+2)=x^4+4x^3-x^2-16x-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+3)(x-2)(x+1)(x+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-2x+3x-6)(x+1)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+x-6)(x+1)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+x^2+x^2+x-6x-6)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3+2x^2-5x-6)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4+4x^3-x^2-16x-12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+3}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x+3}\right) \cdot \left( x-2\right) = x^2-2x+3x-6 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-2x} + \color{blue}{3x} -6 = x^2+ \color{blue}{x} -6 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+x-6}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x^2+x-6}\right) \cdot \left( x+1\right) = x^3+x^2+x^2+x-6x-6 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{x^2} + \color{blue}{x^2} + \color{red}{x} \color{red}{-6x} -6 = x^3+ \color{blue}{2x^2} \color{red}{-5x} -6 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3+2x^2-5x-6}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x^3+2x^2-5x-6}\right) \cdot \left( x+2\right) = x^4+2x^3+2x^3+4x^2-5x^2-10x-6x-12 $$ |
| ⑥ | Combine like terms: $$ x^4+ \color{blue}{2x^3} + \color{blue}{2x^3} + \color{red}{4x^2} \color{red}{-5x^2} \color{green}{-10x} \color{green}{-6x} -12 = x^4+ \color{blue}{4x^3} \color{red}{-x^2} \color{green}{-16x} -12 $$ |
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