Answer
$$(2x+3)^2+8\cdot(3-x)=4x^2+4x+33$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x+3)^2+8\cdot(3-x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4x^2+12x+9+8\cdot(3-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^2+12x+9+24-8x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^2+4x+33\end{aligned} $$ | |
| ① | Find $ \left(2x+3\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2x } $ and $ B = \color{red}{ 3 }$. $$ \begin{aligned}\left(2x+3\right)^2 = \color{blue}{\left( 2x \right)^2} +2 \cdot 2x \cdot 3 + \color{red}{3^2} = 4x^2+12x+9\end{aligned} $$ |
| ② | Multiply $ \color{blue}{8} $ by $ \left( 3-x\right) $ $$ \color{blue}{8} \cdot \left( 3-x\right) = 24-8x $$ |
| ③ | Combine like terms: $$ 4x^2+ \color{blue}{12x} + \color{red}{9} + \color{red}{24} \color{blue}{-8x} = 4x^2+ \color{blue}{4x} + \color{red}{33} $$ |
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