Answer
$$4\cdot(1-x^2)-3(x^2-3x-2)=-7x^2+9x+10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4\cdot(1-x^2)-3(x^2-3x-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4-4x^2-(3x^2-9x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4-4x^2-3x^2+9x+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-7x^2+9x+10\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4} $ by $ \left( 1-x^2\right) $ $$ \color{blue}{4} \cdot \left( 1-x^2\right) = 4-4x^2 $$Multiply $ \color{blue}{3} $ by $ \left( x^2-3x-2\right) $ $$ \color{blue}{3} \cdot \left( x^2-3x-2\right) = 3x^2-9x-6 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 3x^2-9x-6 \right) = -3x^2+9x+6 $$ |
| ③ | Combine like terms: $$ \color{blue}{4} \color{red}{-4x^2} \color{red}{-3x^2} +9x+ \color{blue}{6} = \color{red}{-7x^2} +9x+ \color{blue}{10} $$ |
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