Question
Answer
$$-4x(x-2)^2(x-1)=-4x^4+20x^3-32x^2+16x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-4x(x-2)^2(x-1)& \xlongequal{ }-4x(x^2-4x+4)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ }-(4x^3-16x^2+16x)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(4x^4-4x^3-16x^3+16x^2+16x^2-16x) \xlongequal{ } \\[1 em] & \xlongequal{ }-(4x^4-20x^3+32x^2-16x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-4x^4+20x^3-32x^2+16x\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4x^3-16x^2+16x}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{4x^3-16x^2+16x}\right) \cdot \left( x-1\right) = 4x^4-4x^3-16x^3+16x^2+16x^2-16x $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(4x^4-20x^3+32x^2-16x \right) = -4x^4+20x^3-32x^2+16x $$ |
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