Question
Answer
$$4(2+x)^2+2\cdot(2+x)-20=4x^2+18x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4(2+x)^2+2\cdot(2+x)-20& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4(4+4x+x^2)+2\cdot(2+x)-20 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}16+16x+4x^2+4+2x-20 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^2+18x+20-20 \xlongequal{ } \\[1 em] & \xlongequal{ }4x^2+18x+ \cancel{20} -\cancel{20} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4x^2+18x\end{aligned} $$ | |
| ① | Find $ \left(2+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}{ 2 } $ and $ B = \color{red}{ x }$. $$ \begin{aligned}\left(2+x\right)^2 = \color{blue}{2^2} +2 \cdot 2 \cdot x + \color{red}{x^2} = 4+4x+x^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{4} $ by $ \left( 4+4x+x^2\right) $ $$ \color{blue}{4} \cdot \left( 4+4x+x^2\right) = 16+16x+4x^2 $$Multiply $ \color{blue}{2} $ by $ \left( 2+x\right) $ $$ \color{blue}{2} \cdot \left( 2+x\right) = 4+2x $$ |
| ③ | Combine like terms: $$ \color{blue}{16} + \color{red}{16x} +4x^2+ \color{blue}{4} + \color{red}{2x} = 4x^2+ \color{red}{18x} + \color{blue}{20} $$ |
| ④ | Combine like terms: $$ 4x^2+18x+ \, \color{blue}{ \cancel{20}} \, \, \color{blue}{ -\cancel{20}} \, = 4x^2+18x $$ |
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