Answer
$$(3x+2)^2-3(x+4)+(x-4)^2=10x^2+x+8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x+2)^2-3(x+4)+(x-4)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9x^2+12x+4-3(x+4)+x^2-8x+16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9x^2+12x+4-(3x+12)+x^2-8x+16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}9x^2+12x+4-3x-12+x^2-8x+16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}9x^2+9x-8+x^2-8x+16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}10x^2+x+8\end{aligned} $$ | |
| 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 }$. $$ \begin{aligned}\left(3x+2\right)^2 = \color{blue}{\left( 3x \right)^2} +2 \cdot 3x \cdot 2 + \color{red}{2^2} = 9x^2+12x+4\end{aligned} $$Find $ \left(x-4\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 4 }$. $$ \begin{aligned}\left(x-4\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 4 + \color{red}{4^2} = x^2-8x+16\end{aligned} $$ |
| ② | Multiply $ \color{blue}{3} $ by $ \left( x+4\right) $ $$ \color{blue}{3} \cdot \left( x+4\right) = 3x+12 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 3x+12 \right) = -3x-12 $$ |
| ④ | Combine like terms: $$ 9x^2+ \color{blue}{12x} + \color{red}{4} \color{blue}{-3x} \color{red}{-12} = 9x^2+ \color{blue}{9x} \color{red}{-8} $$ |
| ⑤ | Combine like terms: $$ \color{blue}{9x^2} + \color{red}{9x} \color{green}{-8} + \color{blue}{x^2} \color{red}{-8x} + \color{green}{16} = \color{blue}{10x^2} + \color{red}{x} + \color{green}{8} $$ |
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