Question
Answer
$$3(x-2)^2-5(x-2)+8=3x^2-17x+30$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(x-2)^2-5(x-2)+8& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3(x^2-4x+4)-5(x-2)+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^2-12x+12-(5x-10)+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^2-12x+12-5x+10+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x^2-17x+30\end{aligned} $$ | |
| 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}{5} $ by $ \left( x-2\right) $ $$ \color{blue}{5} \cdot \left( x-2\right) = 5x-10 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 5x-10 \right) = -5x+10 $$ |
| ④ | Combine like terms: $$ 3x^2 \color{blue}{-12x} + \color{red}{12} \color{blue}{-5x} + \color{green}{10} + \color{green}{8} = 3x^2 \color{blue}{-17x} + \color{green}{30} $$ |
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