Question
Answer
$$(2-x)^3-(2-x)=-x^3+6x^2-11x+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2-x)^3-(2-x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8-12x+6x^2-x^3-(2-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8-12x+6x^2-x^3-2+x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-x^3+6x^2-11x+6\end{aligned} $$ | |
| ① | Find $ \left(2-x\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 2 $ and $ B = x $. $$ \left(2-x\right)^3 = 2^3-3 \cdot 2^2 \cdot x + 3 \cdot 2 \cdot x^2-x^3 = 8-12x+6x^2-x^3 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2-x \right) = -2+x $$ |
| ③ | Combine like terms: $$ \color{blue}{8} \color{red}{-12x} +6x^2-x^3 \color{blue}{-2} + \color{red}{x} = -x^3+6x^2 \color{red}{-11x} + \color{blue}{6} $$ |
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