Question
Answer
$$(7+x)(x+2)(x+3)=x^3+12x^2+41x+42$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7+x)(x+2)(x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(7x+14+x^2+2x)(x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+9x+14)(x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+3x^2+9x^2+27x+14x+42 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+12x^2+41x+42\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{7+x}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{7+x}\right) \cdot \left( x+2\right) = 7x+14+x^2+2x $$ |
| ② | Combine like terms: $$ \color{blue}{7x} +14+x^2+ \color{blue}{2x} = x^2+ \color{blue}{9x} +14 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+9x+14}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x^2+9x+14}\right) \cdot \left( x+3\right) = x^3+3x^2+9x^2+27x+14x+42 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{3x^2} + \color{blue}{9x^2} + \color{red}{27x} + \color{red}{14x} +42 = x^3+ \color{blue}{12x^2} + \color{red}{41x} +42 $$ |
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