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