Question
Answer
$$4(x^2-2x+5)-(2x^2+3x-2)=2x^2-11x+22$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4(x^2-2x+5)-(2x^2+3x-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4x^2-8x+20-(2x^2+3x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^2-8x+20-2x^2-3x+2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2-11x+22\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4} $ by $ \left( x^2-2x+5\right) $ $$ \color{blue}{4} \cdot \left( x^2-2x+5\right) = 4x^2-8x+20 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x^2+3x-2 \right) = -2x^2-3x+2 $$ |
| ③ | Combine like terms: $$ \color{blue}{4x^2} \color{red}{-8x} + \color{green}{20} \color{blue}{-2x^2} \color{red}{-3x} + \color{green}{2} = \color{blue}{2x^2} \color{red}{-11x} + \color{green}{22} $$ |
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