Question
Answer
$$8x-3(2x-4)(x-6)=-6x^2+56x-72$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}8x-3(2x-4)(x-6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8x-(6x-12)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8x-(6x^2-36x-12x+72) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8x-(6x^2-48x+72) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}8x-6x^2+48x-72 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-6x^2+56x-72\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( 2x-4\right) $ $$ \color{blue}{3} \cdot \left( 2x-4\right) = 6x-12 $$ |
| ② | Multiply each term of $ \left( \color{blue}{6x-12}\right) $ by each term in $ \left( x-6\right) $. $$ \left( \color{blue}{6x-12}\right) \cdot \left( x-6\right) = 6x^2-36x-12x+72 $$ |
| ③ | Combine like terms: $$ 6x^2 \color{blue}{-36x} \color{blue}{-12x} +72 = 6x^2 \color{blue}{-48x} +72 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6x^2-48x+72 \right) = -6x^2+48x-72 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{8x} -6x^2+ \color{blue}{48x} -72 = -6x^2+ \color{blue}{56x} -72 $$ |
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