Answer
$$(3x-2y)^2-2(2x+3y)(x-y)=5x^2-14xy+10y^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x-2y)^2-2(2x+3y)(x-y)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9x^2-12xy+4y^2-2(2x+3y)(x-y) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9x^2-12xy+4y^2-(4x+6y)(x-y) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}9x^2-12xy+4y^2-(4x^2-4xy+6xy-6y^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}9x^2-12xy+4y^2-(4x^2+2xy-6y^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}9x^2-12xy+4y^2-4x^2-2xy+6y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}5x^2-14xy+10y^2\end{aligned} $$ | |
| ① | Find $ \left(3x-2y\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 2y }$. $$ \begin{aligned}\left(3x-2y\right)^2 = \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 2y + \color{red}{\left( 2y \right)^2} = 9x^2-12xy+4y^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( 2x+3y\right) $ $$ \color{blue}{2} \cdot \left( 2x+3y\right) = 4x+6y $$ |
| ③ | Multiply each term of $ \left( \color{blue}{4x+6y}\right) $ by each term in $ \left( x-y\right) $. $$ \left( \color{blue}{4x+6y}\right) \cdot \left( x-y\right) = 4x^2-4xy+6xy-6y^2 $$ |
| ④ | Combine like terms: $$ 4x^2 \color{blue}{-4xy} + \color{blue}{6xy} -6y^2 = 4x^2+ \color{blue}{2xy} -6y^2 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4x^2+2xy-6y^2 \right) = -4x^2-2xy+6y^2 $$ |
| ⑥ | Combine like terms: $$ \color{blue}{9x^2} \color{red}{-12xy} + \color{green}{4y^2} \color{blue}{-4x^2} \color{red}{-2xy} + \color{green}{6y^2} = \color{blue}{5x^2} \color{red}{-14xy} + \color{green}{10y^2} $$ |
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