Question
Answer
$$(3n+4)(5n+2)+5(n+7)=15n^2+31n+43$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3n+4)(5n+2)+5(n+7)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}15n^2+6n+20n+8+5n+35 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}15n^2+26n+8+5n+35 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}15n^2+31n+43\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3n+4}\right) $ by each term in $ \left( 5n+2\right) $. $$ \left( \color{blue}{3n+4}\right) \cdot \left( 5n+2\right) = 15n^2+6n+20n+8 $$Multiply $ \color{blue}{5} $ by $ \left( n+7\right) $ $$ \color{blue}{5} \cdot \left( n+7\right) = 5n+35 $$ |
| ② | Combine like terms: $$ 15n^2+ \color{blue}{6n} + \color{blue}{20n} +8 = 15n^2+ \color{blue}{26n} +8 $$ |
| ③ | Combine like terms: $$ 15n^2+ \color{blue}{26n} + \color{red}{8} + \color{blue}{5n} + \color{red}{35} = 15n^2+ \color{blue}{31n} + \color{red}{43} $$ |
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