Question
Answer
$$(x-1)(x+5)(x^2+4x-4)=x^4+8x^3+7x^2-36x+20$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-1)(x+5)(x^2+4x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+5x-x-5)(x^2+4x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+4x-5)(x^2+4x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4+8x^3+7x^2-36x+20\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x+5\right) $. $$ \left( \color{blue}{x-1}\right) \cdot \left( x+5\right) = x^2+5x-x-5 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{5x} \color{blue}{-x} -5 = x^2+ \color{blue}{4x} -5 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+4x-5}\right) $ by each term in $ \left( x^2+4x-4\right) $. $$ \left( \color{blue}{x^2+4x-5}\right) \cdot \left( x^2+4x-4\right) = x^4+4x^3-4x^2+4x^3+16x^2-16x-5x^2-20x+20 $$ |
| ④ | Combine like terms: $$ x^4+ \color{blue}{4x^3} \color{red}{-4x^2} + \color{blue}{4x^3} + \color{green}{16x^2} \color{orange}{-16x} \color{green}{-5x^2} \color{orange}{-20x} +20 = \\ = x^4+ \color{blue}{8x^3} + \color{green}{7x^2} \color{orange}{-36x} +20 $$ |
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