Question
Answer
$$-x(x-4)^2(2x-1)=-2x^4+17x^3-40x^2+16x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-x(x-4)^2(2x-1)& \xlongequal{ }-x(x^2-8x+16)(2x-1) \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^3-8x^2+16x)(2x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(2x^4-x^3-16x^3+8x^2+32x^2-16x) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^4-17x^3+40x^2-16x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-2x^4+17x^3-40x^2+16x\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^3-8x^2+16x}\right) $ by each term in $ \left( 2x-1\right) $. $$ \left( \color{blue}{x^3-8x^2+16x}\right) \cdot \left( 2x-1\right) = 2x^4-x^3-16x^3+8x^2+32x^2-16x $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(2x^4-17x^3+40x^2-16x \right) = -2x^4+17x^3-40x^2+16x $$ |
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