Question
Answer
$$(x-2)(x+7)(x-5)(x+8)=x^4+8x^3-39x^2-242x+560$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(x+7)(x-5)(x+8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+7x-2x-14)(x-5)(x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+5x-14)(x-5)(x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3-5x^2+5x^2-25x-14x+70)(x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3-39x+70)(x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^4+8x^3-39x^2-312x+70x+560 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4+8x^3-39x^2-242x+560\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( x+7\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( x+7\right) = x^2+7x-2x-14 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{7x} \color{blue}{-2x} -14 = x^2+ \color{blue}{5x} -14 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+5x-14}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x^2+5x-14}\right) \cdot \left( x-5\right) = x^3 -\cancel{5x^2}+ \cancel{5x^2}-25x-14x+70 $$ |
| ④ | Combine like terms: $$ x^3 \, \color{blue}{ -\cancel{5x^2}} \,+ \, \color{blue}{ \cancel{5x^2}} \, \color{green}{-25x} \color{green}{-14x} +70 = x^3 \color{green}{-39x} +70 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3-39x+70}\right) $ by each term in $ \left( x+8\right) $. $$ \left( \color{blue}{x^3-39x+70}\right) \cdot \left( x+8\right) = x^4+8x^3-39x^2-312x+70x+560 $$ |
| ⑥ | Combine like terms: $$ x^4+8x^3-39x^2 \color{blue}{-312x} + \color{blue}{70x} +560 = x^4+8x^3-39x^2 \color{blue}{-242x} +560 $$ |
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