Question
Answer
$$-2(x-1)(x+4)(x+1)(x-3)=-2x^4-2x^3+26x^2+2x-24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-2(x-1)(x+4)(x+1)(x-3)& \xlongequal{ }-(2x-2)(x+4)(x+1)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^2+8x-2x-8)(x+1)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^2+6x-8)(x+1)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^3+2x^2+6x^2+6x-8x-8)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^3+8x^2-2x-8)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(2x^4+2x^3-26x^2-2x+24) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2x^4-2x^3+26x^2+2x-24\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x^3+8x^2-2x-8}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{2x^3+8x^2-2x-8}\right) \cdot \left( x-3\right) = 2x^4-6x^3+8x^3-24x^2-2x^2+6x-8x+24 $$ |
| ② | Combine like terms: $$ 2x^4 \color{blue}{-6x^3} + \color{blue}{8x^3} \color{red}{-24x^2} \color{red}{-2x^2} + \color{green}{6x} \color{green}{-8x} +24 = 2x^4+ \color{blue}{2x^3} \color{red}{-26x^2} \color{green}{-2x} +24 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(2x^4+2x^3-26x^2-2x+24 \right) = -2x^4-2x^3+26x^2+2x-24 $$ |
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