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