Question
Answer
$$(x-10)(x+2)(x+3)(x+4)=x^4-x^3-64x^2-236x-240$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-10)(x+2)(x+3)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x-10x-20)(x+3)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-8x-20)(x+3)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+3x^2-8x^2-24x-20x-60)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3-5x^2-44x-60)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4-x^3-64x^2-236x-240\end{aligned} $$ | |
| 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: $$ x^2+ \color{blue}{2x} \color{blue}{-10x} -20 = x^2 \color{blue}{-8x} -20 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-8x-20}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x^2-8x-20}\right) \cdot \left( x+3\right) = x^3+3x^2-8x^2-24x-20x-60 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{3x^2} \color{blue}{-8x^2} \color{red}{-24x} \color{red}{-20x} -60 = x^3 \color{blue}{-5x^2} \color{red}{-44x} -60 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3-5x^2-44x-60}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x^3-5x^2-44x-60}\right) \cdot \left( x+4\right) = x^4+4x^3-5x^3-20x^2-44x^2-176x-60x-240 $$ |
| ⑥ | Combine like terms: $$ x^4+ \color{blue}{4x^3} \color{blue}{-5x^3} \color{red}{-20x^2} \color{red}{-44x^2} \color{green}{-176x} \color{green}{-60x} -240 = x^4 \color{blue}{-x^3} \color{red}{-64x^2} \color{green}{-236x} -240 $$ |
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