Question
Answer
$$(1-x)^2x+(1-x)x^2=-x^2+x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1-x)^2x+(1-x)x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1-2x+x^2)x+(1-x)x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x-2x^2+x^3+x^2-x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-x^2+x\end{aligned} $$ | |
| 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 | $$ \left( \color{blue}{1-2x+x^2}\right) \cdot x = x-2x^2+x^3 $$$$ \left( \color{blue}{1-x}\right) \cdot x^2 = x^2-x^3 $$ |
| ③ | Combine like terms: $$ x \color{blue}{-2x^2} + \, \color{red}{ \cancel{x^3}} \,+ \color{blue}{x^2} \, \color{red}{ -\cancel{x^3}} \, = \color{blue}{-x^2} +x $$ |
This page was created using
Simplify polynomials calculator