Question
Answer
$$(x+1)(x+1)(x-5)=x^3-3x^2-9x-5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+1)(x+1)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+x+x+1)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+2x+1)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-5x^2+2x^2-10x+x-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-3x^2-9x-5\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+1}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x+1}\right) \cdot \left( x+1\right) = x^2+x+x+1 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{x} + \color{blue}{x} +1 = x^2+ \color{blue}{2x} +1 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+2x+1}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x^2+2x+1}\right) \cdot \left( x-5\right) = x^3-5x^2+2x^2-10x+x-5 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-5x^2} + \color{blue}{2x^2} \color{red}{-10x} + \color{red}{x} -5 = x^3 \color{blue}{-3x^2} \color{red}{-9x} -5 $$ |
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