Question
Answer
$$(x+4)(x+5)(x+9)=x^3+18x^2+101x+180$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+4)(x+5)(x+9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+5x+4x+20)(x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+9x+20)(x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+9x^2+9x^2+81x+20x+180 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+18x^2+101x+180\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+4}\right) $ by each term in $ \left( x+5\right) $. $$ \left( \color{blue}{x+4}\right) \cdot \left( x+5\right) = x^2+5x+4x+20 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{5x} + \color{blue}{4x} +20 = x^2+ \color{blue}{9x} +20 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+9x+20}\right) $ by each term in $ \left( x+9\right) $. $$ \left( \color{blue}{x^2+9x+20}\right) \cdot \left( x+9\right) = x^3+9x^2+9x^2+81x+20x+180 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{9x^2} + \color{blue}{9x^2} + \color{red}{81x} + \color{red}{20x} +180 = x^3+ \color{blue}{18x^2} + \color{red}{101x} +180 $$ |
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