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