Question
Answer
$$(x+10)(x+7)(x+1)(x-4)=x^4+14x^3+15x^2-278x-280$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+10)(x+7)(x+1)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+7x+10x+70)(x+1)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+17x+70)(x+1)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+x^2+17x^2+17x+70x+70)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3+18x^2+87x+70)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4+14x^3+15x^2-278x-280\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+10}\right) $ by each term in $ \left( x+7\right) $. $$ \left( \color{blue}{x+10}\right) \cdot \left( x+7\right) = x^2+7x+10x+70 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{7x} + \color{blue}{10x} +70 = x^2+ \color{blue}{17x} +70 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+17x+70}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x^2+17x+70}\right) \cdot \left( x+1\right) = x^3+x^2+17x^2+17x+70x+70 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{x^2} + \color{blue}{17x^2} + \color{red}{17x} + \color{red}{70x} +70 = x^3+ \color{blue}{18x^2} + \color{red}{87x} +70 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3+18x^2+87x+70}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^3+18x^2+87x+70}\right) \cdot \left( x-4\right) = x^4-4x^3+18x^3-72x^2+87x^2-348x+70x-280 $$ |
| ⑥ | Combine like terms: $$ x^4 \color{blue}{-4x^3} + \color{blue}{18x^3} \color{red}{-72x^2} + \color{red}{87x^2} \color{green}{-348x} + \color{green}{70x} -280 = \\ = x^4+ \color{blue}{14x^3} + \color{red}{15x^2} \color{green}{-278x} -280 $$ |
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