Question
Answer
$$x(4x+3y)-(y-2x)^2=7xy-y^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(4x+3y)-(y-2x)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x(4x+3y)-(1y^2-4xy+4x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^2+3xy-(1y^2-4xy+4x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^2+3xy-y^2+4xy-4x^2 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{4x^2}+3xy-y^2+4xy -\cancel{4x^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}7xy-y^2\end{aligned} $$ | |
| ① | Find $ \left(y-2x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ y } $ and $ B = \color{red}{ 2x }$. $$ \begin{aligned}\left(y-2x\right)^2 = \color{blue}{y^2} -2 \cdot y \cdot 2x + \color{red}{\left( 2x \right)^2} = y^2-4xy+4x^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{x} $ by $ \left( 4x+3y\right) $ $$ \color{blue}{x} \cdot \left( 4x+3y\right) = 4x^2+3xy $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( y^2-4xy+4x^2 \right) = -y^2+4xy-4x^2 $$ |
| ④ | Combine like terms: $$ \, \color{blue}{ \cancel{4x^2}} \,+ \color{green}{3xy} -y^2+ \color{green}{4xy} \, \color{blue}{ -\cancel{4x^2}} \, = \color{green}{7xy} -y^2 $$ |
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