Question
Answer
$$3(5x-4)(8x-2)+7(x-9)=120x^2-119x-39$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(5x-4)(8x-2)+7(x-9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(15x-12)(8x-2)+7x-63 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}120x^2-30x-96x+24+7x-63 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}120x^2-126x+24+7x-63 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}120x^2-119x-39\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( 5x-4\right) $ $$ \color{blue}{3} \cdot \left( 5x-4\right) = 15x-12 $$Multiply $ \color{blue}{7} $ by $ \left( x-9\right) $ $$ \color{blue}{7} \cdot \left( x-9\right) = 7x-63 $$ |
| ② | Multiply each term of $ \left( \color{blue}{15x-12}\right) $ by each term in $ \left( 8x-2\right) $. $$ \left( \color{blue}{15x-12}\right) \cdot \left( 8x-2\right) = 120x^2-30x-96x+24 $$ |
| ③ | Combine like terms: $$ 120x^2 \color{blue}{-30x} \color{blue}{-96x} +24 = 120x^2 \color{blue}{-126x} +24 $$ |
| ④ | Combine like terms: $$ 120x^2 \color{blue}{-126x} + \color{red}{24} + \color{blue}{7x} \color{red}{-63} = 120x^2 \color{blue}{-119x} \color{red}{-39} $$ |
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