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