Answer
$$(x+11)(x-5)(x-5)(x-10)=x^4-9x^3-95x^2+1125x-2750$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+11)(x-5)(x-5)(x-10)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-5x+11x-55)(x-5)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+6x-55)(x-5)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3-5x^2+6x^2-30x-55x+275)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3+x^2-85x+275)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4-9x^3-95x^2+1125x-2750\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+11}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x+11}\right) \cdot \left( x-5\right) = x^2-5x+11x-55 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-5x} + \color{blue}{11x} -55 = x^2+ \color{blue}{6x} -55 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+6x-55}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x^2+6x-55}\right) \cdot \left( x-5\right) = x^3-5x^2+6x^2-30x-55x+275 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-5x^2} + \color{blue}{6x^2} \color{red}{-30x} \color{red}{-55x} +275 = x^3+ \color{blue}{x^2} \color{red}{-85x} +275 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3+x^2-85x+275}\right) $ by each term in $ \left( x-10\right) $. $$ \left( \color{blue}{x^3+x^2-85x+275}\right) \cdot \left( x-10\right) = x^4-10x^3+x^3-10x^2-85x^2+850x+275x-2750 $$ |
| ⑥ | Combine like terms: $$ x^4 \color{blue}{-10x^3} + \color{blue}{x^3} \color{red}{-10x^2} \color{red}{-85x^2} + \color{green}{850x} + \color{green}{275x} -2750 = \\ = x^4 \color{blue}{-9x^3} \color{red}{-95x^2} + \color{green}{1125x} -2750 $$ |
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