Question
Answer
$$2x(x-1)^3=2x^4-6x^3+6x^2-2x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2x(x-1)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2x(x^3-3x^2+3x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^4-6x^3+6x^2-2x\end{aligned} $$ | |
| ① | Find $ \left(x-1\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = x $ and $ B = 1 $. $$ \left(x-1\right)^3 = x^3-3 \cdot x^2 \cdot 1 + 3 \cdot x \cdot 1^2-1^3 = x^3-3x^2+3x-1 $$ |
| ② | Multiply $ \color{blue}{2x} $ by $ \left( x^3-3x^2+3x-1\right) $ $$ \color{blue}{2x} \cdot \left( x^3-3x^2+3x-1\right) = 2x^4-6x^3+6x^2-2x $$ |
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