Answer
$$x-4-2(x+5)(x-3)=-2x^2-3x+26$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x-4-2(x+5)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x-4-(2x+10)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x-4-(2x^2-6x+10x-30) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x-4-(2x^2+4x-30) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x-4-2x^2-4x+30 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-2x^2-3x+26\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( x+5\right) $ $$ \color{blue}{2} \cdot \left( x+5\right) = 2x+10 $$ |
| ② | Multiply each term of $ \left( \color{blue}{2x+10}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{2x+10}\right) \cdot \left( x-3\right) = 2x^2-6x+10x-30 $$ |
| ③ | Combine like terms: $$ 2x^2 \color{blue}{-6x} + \color{blue}{10x} -30 = 2x^2+ \color{blue}{4x} -30 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x^2+4x-30 \right) = -2x^2-4x+30 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{x} \color{red}{-4} -2x^2 \color{blue}{-4x} + \color{red}{30} = -2x^2 \color{blue}{-3x} + \color{red}{26} $$ |
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