Question
Answer
$$(x+10)(x+2)(x+2)(x-6)=x^4+8x^3-40x^2-224x-240$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+10)(x+2)(x+2)(x-6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x+10x+20)(x+2)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+12x+20)(x+2)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+2x^2+12x^2+24x+20x+40)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3+14x^2+44x+40)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4+8x^3-40x^2-224x-240\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+10}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x+10}\right) \cdot \left( x+2\right) = x^2+2x+10x+20 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{2x} + \color{blue}{10x} +20 = x^2+ \color{blue}{12x} +20 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+12x+20}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x^2+12x+20}\right) \cdot \left( x+2\right) = x^3+2x^2+12x^2+24x+20x+40 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{2x^2} + \color{blue}{12x^2} + \color{red}{24x} + \color{red}{20x} +40 = x^3+ \color{blue}{14x^2} + \color{red}{44x} +40 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3+14x^2+44x+40}\right) $ by each term in $ \left( x-6\right) $. $$ \left( \color{blue}{x^3+14x^2+44x+40}\right) \cdot \left( x-6\right) = x^4-6x^3+14x^3-84x^2+44x^2-264x+40x-240 $$ |
| ⑥ | Combine like terms: $$ x^4 \color{blue}{-6x^3} + \color{blue}{14x^3} \color{red}{-84x^2} + \color{red}{44x^2} \color{green}{-264x} + \color{green}{40x} -240 = \\ = x^4+ \color{blue}{8x^3} \color{red}{-40x^2} \color{green}{-224x} -240 $$ |
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