Question
Answer
$$5x^2-2xy+6x-7y+9xy-5y^2+7y-5+x^2+y^2-x+2-8x^2+xy-3y^2+2x-10=-2x^2+8xy-7y^2+7x-13$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5x^2-2xy+6x-7y+9xy-5y^2+7y-5+x^2+y^2-x+2-8x^2+xy-3y^2+2x-10& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5x^2+7xy-5y^2+6x-5+x^2+y^2-x+2-8x^2+xy-3y^2+2x-10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6x^2+7xy-4y^2+5x-3-8x^2+xy-3y^2+2x-10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2x^2+8xy-7y^2+7x-13\end{aligned} $$ | |
| ① | Combine like terms: $$ 5x^2 \color{blue}{-2xy} +6x \, \color{red}{ -\cancel{7y}} \,+ \color{blue}{9xy} -5y^2+ \, \color{red}{ \cancel{7y}} \,-5 = 5x^2+ \color{blue}{7xy} -5y^2+6x-5 $$ |
| ② | Combine like terms: $$ \color{blue}{5x^2} +7xy \color{red}{-5y^2} + \color{green}{6x} \color{orange}{-5} + \color{blue}{x^2} + \color{red}{y^2} \color{green}{-x} + \color{orange}{2} = \\ = \color{blue}{6x^2} +7xy \color{red}{-4y^2} + \color{green}{5x} \color{orange}{-3} $$ |
| ③ | Combine like terms: $$ \color{blue}{6x^2} + \color{red}{7xy} \color{green}{-4y^2} + \color{orange}{5x} \color{blue}{-3} \color{blue}{-8x^2} + \color{red}{xy} \color{green}{-3y^2} + \color{orange}{2x} \color{blue}{-10} = \\ = \color{blue}{-2x^2} + \color{red}{8xy} \color{green}{-7y^2} + \color{orange}{7x} \color{blue}{-13} $$ |
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