Question
Answer
$$4(x-3y)(x+3y)-(2x-y)^2=4xy-37y^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4(x-3y)(x+3y)-(2x-y)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4(x-3y)(x+3y)-(4x^2-4xy+y^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(4x-12y)(x+3y)-(4x^2-4xy+y^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^2+12xy-12xy-36y^2-(4x^2-4xy+y^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4x^2-36y^2-(4x^2-4xy+y^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}4x^2-36y^2-4x^2+4xy-y^2 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{4x^2}-36y^2 -\cancel{4x^2}+4xy-y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}4xy-37y^2\end{aligned} $$ | |
| ① | Find $ \left(2x-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}{ 2x } $ and $ B = \color{red}{ y }$. $$ \begin{aligned}\left(2x-y\right)^2 = \color{blue}{\left( 2x \right)^2} -2 \cdot 2x \cdot y + \color{red}{y^2} = 4x^2-4xy+y^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{4} $ by $ \left( x-3y\right) $ $$ \color{blue}{4} \cdot \left( x-3y\right) = 4x-12y $$ |
| ③ | Multiply each term of $ \left( \color{blue}{4x-12y}\right) $ by each term in $ \left( x+3y\right) $. $$ \left( \color{blue}{4x-12y}\right) \cdot \left( x+3y\right) = 4x^2+ \cancel{12xy} -\cancel{12xy}-36y^2 $$ |
| ④ | Combine like terms: $$ 4x^2+ \, \color{blue}{ \cancel{12xy}} \, \, \color{blue}{ -\cancel{12xy}} \,-36y^2 = 4x^2-36y^2 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4x^2-4xy+y^2 \right) = -4x^2+4xy-y^2 $$ |
| ⑥ | Combine like terms: $$ \, \color{blue}{ \cancel{4x^2}} \, \color{green}{-36y^2} \, \color{blue}{ -\cancel{4x^2}} \,+4xy \color{green}{-y^2} = 4xy \color{green}{-37y^2} $$ |
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