Question
Answer
$$8(5+x)^2+7\cdot(5+x)+6=8x^2+87x+241$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}8(5+x)^2+7\cdot(5+x)+6& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8(25+10x+x^2)+7\cdot(5+x)+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}200+80x+8x^2+35+7x+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8x^2+87x+235+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}8x^2+87x+241\end{aligned} $$ | |
| ① | Find $ \left(5+x\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 5 } $ and $ B = \color{red}{ x }$. $$ \begin{aligned}\left(5+x\right)^2 = \color{blue}{5^2} +2 \cdot 5 \cdot x + \color{red}{x^2} = 25+10x+x^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{8} $ by $ \left( 25+10x+x^2\right) $ $$ \color{blue}{8} \cdot \left( 25+10x+x^2\right) = 200+80x+8x^2 $$Multiply $ \color{blue}{7} $ by $ \left( 5+x\right) $ $$ \color{blue}{7} \cdot \left( 5+x\right) = 35+7x $$ |
| ③ | Combine like terms: $$ \color{blue}{200} + \color{red}{80x} +8x^2+ \color{blue}{35} + \color{red}{7x} = 8x^2+ \color{red}{87x} + \color{blue}{235} $$ |
| ④ | Combine like terms: $$ 8x^2+87x+ \color{blue}{235} + \color{blue}{6} = 8x^2+87x+ \color{blue}{241} $$ |
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