Question
Answer
$$(-x^2+2x)^2=x^4-4x^3+4x^2$$
Explanation
| $$ \begin{aligned}(-x^2+2x)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^4-4x^3+4x^2\end{aligned} $$ | |
| ① | Find $ \left(-x^2+2x\right)^2 $ in two steps. S1: Change all signs inside bracket. S2: Apply formula $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x^2 } $ and $ B = \color{red}{ 2x }$. $$ \begin{aligned}\left(-x^2+2x\right)^2& \xlongequal{ S1 } \left(x^2-2x\right)^2 \xlongequal{ S2 } \color{blue}{\left( x^2 \right)^2} -2 \cdot x^2 \cdot 2x + \color{red}{\left( 2x \right)^2} = \\[1 em] & = x^4-4x^3+4x^2\end{aligned} $$ |
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