Question
Answer
$$(x+60)x(x+1)(x+10)=x^4+71x^3+670x^2+600x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+60)x(x+1)(x+10)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+60x)(x+1)(x+10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^3+x^2+60x^2+60x)(x+10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+61x^2+60x)(x+10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4+10x^3+61x^3+610x^2+60x^2+600x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^4+71x^3+670x^2+600x\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{x+60}\right) \cdot x = x^2+60x $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2+60x}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x^2+60x}\right) \cdot \left( x+1\right) = x^3+x^2+60x^2+60x $$ |
| ③ | Combine like terms: $$ x^3+ \color{blue}{x^2} + \color{blue}{60x^2} +60x = x^3+ \color{blue}{61x^2} +60x $$ |
| ④ | Multiply each term of $ \left( \color{blue}{x^3+61x^2+60x}\right) $ by each term in $ \left( x+10\right) $. $$ \left( \color{blue}{x^3+61x^2+60x}\right) \cdot \left( x+10\right) = x^4+10x^3+61x^3+610x^2+60x^2+600x $$ |
| ⑤ | Combine like terms: $$ x^4+ \color{blue}{10x^3} + \color{blue}{61x^3} + \color{red}{610x^2} + \color{red}{60x^2} +600x = x^4+ \color{blue}{71x^3} + \color{red}{670x^2} +600x $$ |
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