Question
Answer
$$(3x+2)^2+8(3x+2)+12=9x^2+36x+32$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x+2)^2+8(3x+2)+12& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9x^2+12x+4+8(3x+2)+12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9x^2+12x+4+24x+16+12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}9x^2+36x+20+12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}9x^2+36x+32\end{aligned} $$ | |
| ① | Find $ \left(3x+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(3x+2\right)^2 = \color{blue}{\left( 3x \right)^2} +2 \cdot 3x \cdot 2 + \color{red}{2^2} = 9x^2+12x+4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{8} $ by $ \left( 3x+2\right) $ $$ \color{blue}{8} \cdot \left( 3x+2\right) = 24x+16 $$ |
| ③ | Combine like terms: $$ 9x^2+ \color{blue}{12x} + \color{red}{4} + \color{blue}{24x} + \color{red}{16} = 9x^2+ \color{blue}{36x} + \color{red}{20} $$ |
| ④ | Combine like terms: $$ 9x^2+36x+ \color{blue}{20} + \color{blue}{12} = 9x^2+36x+ \color{blue}{32} $$ |
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