Answer
$$(x+2)(x-5)+(x+1)(x+4)-(x-3)(x+4)=x^2+x+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)(x-5)+(x+1)(x+4)-(x-3)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2-5x+2x-10+x^2+4x+x+4-(x^2+4x-3x-12) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2-3x-10+x^2+5x+4-(x^2+x-12) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2+2x-6-(x^2+x-12) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^2+2x-6-x^2-x+12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^2+x+6\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+2}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x+2}\right) \cdot \left( x-5\right) = x^2-5x+2x-10 $$Multiply each term of $ \left( \color{blue}{x+1}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x+1}\right) \cdot \left( x+4\right) = x^2+4x+x+4 $$Multiply each term of $ \left( \color{blue}{x-3}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x-3}\right) \cdot \left( x+4\right) = x^2+4x-3x-12 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-5x} + \color{blue}{2x} -10 = x^2 \color{blue}{-3x} -10 $$Combine like terms: $$ x^2+ \color{blue}{4x} + \color{blue}{x} +4 = x^2+ \color{blue}{5x} +4 $$Combine like terms: $$ x^2+ \color{blue}{4x} \color{blue}{-3x} -12 = x^2+ \color{blue}{x} -12 $$ |
| ③ | Combine like terms: $$ \color{blue}{x^2} \color{red}{-3x} \color{green}{-10} + \color{blue}{x^2} + \color{red}{5x} + \color{green}{4} = \color{blue}{2x^2} + \color{red}{2x} \color{green}{-6} $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2+x-12 \right) = -x^2-x+12 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{2x^2} + \color{red}{2x} \color{green}{-6} \color{blue}{-x^2} \color{red}{-x} + \color{green}{12} = \color{blue}{x^2} + \color{red}{x} + \color{green}{6} $$ |
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