Question
Answer
$$(x-2)^2-2(3x-4)=x^2-10x+12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)^2-2(3x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2-4x+4-2(3x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2-4x+4-(6x-8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^2-4x+4-6x+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^2-10x+12\end{aligned} $$ | |
| 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}{2} $ by $ \left( 3x-4\right) $ $$ \color{blue}{2} \cdot \left( 3x-4\right) = 6x-8 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6x-8 \right) = -6x+8 $$ |
| ④ | Combine like terms: $$ x^2 \color{blue}{-4x} + \color{red}{4} \color{blue}{-6x} + \color{red}{8} = x^2 \color{blue}{-10x} + \color{red}{12} $$ |
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