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