Question
Answer
$$x(y-x)^2=x^3-2x^2y+xy^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(y-x)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x(1y^2-2xy+x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}xy^2-2x^2y+x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-2x^2y+xy^2\end{aligned} $$ | |
| ① | Find $ \left(y-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}{ y } $ and $ B = \color{red}{ x }$. $$ \begin{aligned}\left(y-x\right)^2 = \color{blue}{y^2} -2 \cdot y \cdot x + \color{red}{x^2} = y^2-2xy+x^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{x} $ by $ \left( y^2-2xy+x^2\right) $ $$ \color{blue}{x} \cdot \left( y^2-2xy+x^2\right) = xy^2-2x^2y+x^3 $$ |
| ③ | Combine like terms: $$ x^3-2x^2y+xy^2 = x^3-2x^2y+xy^2 $$ |
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