Answer
$$(x+2y)^2-(x-3y)^2=10xy-5y^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2y)^2-(x-3y)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2+4xy+4y^2-(x^2-6xy+9y^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2+4xy+4y^2-x^2+6xy-9y^2 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{x^2}+4xy+4y^2 -\cancel{x^2}+6xy-9y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10xy-5y^2\end{aligned} $$ | |
| ① | Find $ \left(x+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}{ x } $ and $ B = \color{red}{ 2y }$. $$ \begin{aligned}\left(x+2y\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 2y + \color{red}{\left( 2y \right)^2} = x^2+4xy+4y^2\end{aligned} $$Find $ \left(x-3y\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}{ 3y }$. $$ \begin{aligned}\left(x-3y\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 3y + \color{red}{\left( 3y \right)^2} = x^2-6xy+9y^2\end{aligned} $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2-6xy+9y^2 \right) = -x^2+6xy-9y^2 $$ |
| ③ | Combine like terms: $$ \, \color{blue}{ \cancel{x^2}} \,+ \color{green}{4xy} + \color{orange}{4y^2} \, \color{blue}{ -\cancel{x^2}} \,+ \color{green}{6xy} \color{orange}{-9y^2} = \color{green}{10xy} \color{orange}{-5y^2} $$ |
This page was created using
Simplify polynomials calculator