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