Answer
$$3(x-2)^2+2(x-2)+5=3x^2-10x+13$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(x-2)^2+2(x-2)+5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3(x^2-4x+4)+2(x-2)+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^2-12x+12+2x-4+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^2-10x+8+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x^2-10x+13\end{aligned} $$ | |
| ① | Find $ \left(x-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}{ x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(x-2\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 2 + \color{red}{2^2} = x^2-4x+4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{3} $ by $ \left( x^2-4x+4\right) $ $$ \color{blue}{3} \cdot \left( x^2-4x+4\right) = 3x^2-12x+12 $$Multiply $ \color{blue}{2} $ by $ \left( x-2\right) $ $$ \color{blue}{2} \cdot \left( x-2\right) = 2x-4 $$ |
| ③ | Combine like terms: $$ 3x^2 \color{blue}{-12x} + \color{red}{12} + \color{blue}{2x} \color{red}{-4} = 3x^2 \color{blue}{-10x} + \color{red}{8} $$ |
| ④ | Combine like terms: $$ 3x^2-10x+ \color{blue}{8} + \color{blue}{5} = 3x^2-10x+ \color{blue}{13} $$ |
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