Question
Answer
$$(5x-8)(2x+2)(x-3)=10x^3-36x^2+2x+48$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x-8)(2x+2)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(10x^2+10x-16x-16)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(10x^2-6x-16)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10x^3-30x^2-6x^2+18x-16x+48 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}10x^3-36x^2+2x+48\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5x-8}\right) $ by each term in $ \left( 2x+2\right) $. $$ \left( \color{blue}{5x-8}\right) \cdot \left( 2x+2\right) = 10x^2+10x-16x-16 $$ |
| ② | Combine like terms: $$ 10x^2+ \color{blue}{10x} \color{blue}{-16x} -16 = 10x^2 \color{blue}{-6x} -16 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{10x^2-6x-16}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{10x^2-6x-16}\right) \cdot \left( x-3\right) = 10x^3-30x^2-6x^2+18x-16x+48 $$ |
| ④ | Combine like terms: $$ 10x^3 \color{blue}{-30x^2} \color{blue}{-6x^2} + \color{red}{18x} \color{red}{-16x} +48 = 10x^3 \color{blue}{-36x^2} + \color{red}{2x} +48 $$ |
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