Answer
$$(x+5)(x+1)(x-3)=x^3+3x^2-13x-15$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+5)(x+1)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+x+5x+5)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+6x+5)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-3x^2+6x^2-18x+5x-15 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+3x^2-13x-15\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+5}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x+5}\right) \cdot \left( x+1\right) = x^2+x+5x+5 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{x} + \color{blue}{5x} +5 = x^2+ \color{blue}{6x} +5 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+6x+5}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{x^2+6x+5}\right) \cdot \left( x-3\right) = x^3-3x^2+6x^2-18x+5x-15 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-3x^2} + \color{blue}{6x^2} \color{red}{-18x} + \color{red}{5x} -15 = x^3+ \color{blue}{3x^2} \color{red}{-13x} -15 $$ |
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