Question
Answer
$$(x-1)(x+3)(x+5)=x^3+7x^2+7x-15$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-1)(x+3)(x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+3x-x-3)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+2x-3)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+5x^2+2x^2+10x-3x-15 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+7x^2+7x-15\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x-1}\right) \cdot \left( x+3\right) = x^2+3x-x-3 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{3x} \color{blue}{-x} -3 = x^2+ \color{blue}{2x} -3 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+2x-3}\right) $ by each term in $ \left( x+5\right) $. $$ \left( \color{blue}{x^2+2x-3}\right) \cdot \left( x+5\right) = x^3+5x^2+2x^2+10x-3x-15 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{5x^2} + \color{blue}{2x^2} + \color{red}{10x} \color{red}{-3x} -15 = x^3+ \color{blue}{7x^2} + \color{red}{7x} -15 $$ |
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