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