Question
Answer
$$(y^2-xy)^2=x^2y^2-2xy^3+y^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(y^2-xy)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}y^4-2xy^3+x^2y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2y^2-2xy^3+y^4\end{aligned} $$ | |
| ① | Find $ \left(y^2-xy\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^2 } $ and $ B = \color{red}{ xy }$. $$ \begin{aligned}\left(y^2-xy\right)^2 = \color{blue}{\left( y^2 \right)^2} -2 \cdot y^2 \cdot xy + \color{red}{\left( xy \right)^2} = y^4-2xy^3+x^2y^2\end{aligned} $$ |
| ② | Combine like terms: $$ x^2y^2-2xy^3+y^4 = x^2y^2-2xy^3+y^4 $$ |
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