Answer
$$(x+1)(x+2)(x+5)=x^3+8x^2+17x+10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+1)(x+2)(x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x+x+2)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+3x+2)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+5x^2+3x^2+15x+2x+10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+8x^2+17x+10\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+1}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x+1}\right) \cdot \left( x+2\right) = x^2+2x+x+2 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{2x} + \color{blue}{x} +2 = x^2+ \color{blue}{3x} +2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+3x+2}\right) $ by each term in $ \left( x+5\right) $. $$ \left( \color{blue}{x^2+3x+2}\right) \cdot \left( x+5\right) = x^3+5x^2+3x^2+15x+2x+10 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{5x^2} + \color{blue}{3x^2} + \color{red}{15x} + \color{red}{2x} +10 = x^3+ \color{blue}{8x^2} + \color{red}{17x} +10 $$ |
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