Answer
$$(5a+1)(4a+2)+(a-5)(2a-1)=22a^2+3a+7$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5a+1)(4a+2)+(a-5)(2a-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}20a^2+10a+4a+2+2a^2-a-10a+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}20a^2+14a+2+2a^2-11a+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}22a^2+3a+7\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5a+1}\right) $ by each term in $ \left( 4a+2\right) $. $$ \left( \color{blue}{5a+1}\right) \cdot \left( 4a+2\right) = 20a^2+10a+4a+2 $$Multiply each term of $ \left( \color{blue}{a-5}\right) $ by each term in $ \left( 2a-1\right) $. $$ \left( \color{blue}{a-5}\right) \cdot \left( 2a-1\right) = 2a^2-a-10a+5 $$ |
| ② | Combine like terms: $$ 20a^2+ \color{blue}{10a} + \color{blue}{4a} +2 = 20a^2+ \color{blue}{14a} +2 $$Combine like terms: $$ 2a^2 \color{blue}{-a} \color{blue}{-10a} +5 = 2a^2 \color{blue}{-11a} +5 $$ |
| ③ | Combine like terms: $$ \color{blue}{20a^2} + \color{red}{14a} + \color{green}{2} + \color{blue}{2a^2} \color{red}{-11a} + \color{green}{5} = \color{blue}{22a^2} + \color{red}{3a} + \color{green}{7} $$ |
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