Answer
$$(x+6)(x-8)+(x+16)(x+3)=2x^2+17x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+6)(x-8)+(x+16)(x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2-8x+6x-48+x^2+3x+16x+48 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2-2x-48+x^2+19x+48 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2+17x\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+6}\right) $ by each term in $ \left( x-8\right) $. $$ \left( \color{blue}{x+6}\right) \cdot \left( x-8\right) = x^2-8x+6x-48 $$Multiply each term of $ \left( \color{blue}{x+16}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x+16}\right) \cdot \left( x+3\right) = x^2+3x+16x+48 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-8x} + \color{blue}{6x} -48 = x^2 \color{blue}{-2x} -48 $$Combine like terms: $$ x^2+ \color{blue}{3x} + \color{blue}{16x} +48 = x^2+ \color{blue}{19x} +48 $$ |
| ③ | Combine like terms: $$ \color{blue}{x^2} \color{red}{-2x} \, \color{green}{ -\cancel{48}} \,+ \color{blue}{x^2} + \color{red}{19x} + \, \color{green}{ \cancel{48}} \, = \color{blue}{2x^2} + \color{red}{17x} $$ |
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