Question
Answer
$$(1-x)^3+2\cdot(1-x)x+(1-x)x^2=-2x^3+2x^2-x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1-x)^3+2\cdot(1-x)x+(1-x)x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}1-3x+3x^2-x^3+2\cdot(1-x)x+(1-x)x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1-3x+3x^2-x^3+(2-2x)x+x^2-x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}1-3x+3x^2-x^3+2x-2x^2+x^2-x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-x^3+x^2-x+1+x^2-x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-2x^3+2x^2-x+1\end{aligned} $$ | |
| ① | Find $ \left(1-x\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 1 $ and $ B = x $. $$ \left(1-x\right)^3 = 1^3-3 \cdot 1^2 \cdot x + 3 \cdot 1 \cdot x^2-x^3 = 1-3x+3x^2-x^3 $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( 1-x\right) $ $$ \color{blue}{2} \cdot \left( 1-x\right) = 2-2x $$$$ \left( \color{blue}{1-x}\right) \cdot x^2 = x^2-x^3 $$ |
| ③ | $$ \left( \color{blue}{2-2x}\right) \cdot x = 2x-2x^2 $$ |
| ④ | Combine like terms: $$ 1 \color{blue}{-3x} + \color{red}{3x^2} -x^3+ \color{blue}{2x} \color{red}{-2x^2} = -x^3+ \color{red}{x^2} \color{blue}{-x} +1 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-x^3} + \color{red}{x^2} -x+1+ \color{red}{x^2} \color{blue}{-x^3} = \color{blue}{-2x^3} + \color{red}{2x^2} -x+1 $$ |
This page was created using
Simplify polynomials calculator