Question
Answer
$$(7x-8)(4x+2)(x-5)=28x^3-158x^2+74x+80$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7x-8)(4x+2)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(28x^2+14x-32x-16)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(28x^2-18x-16)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}28x^3-140x^2-18x^2+90x-16x+80 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}28x^3-158x^2+74x+80\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{7x-8}\right) $ by each term in $ \left( 4x+2\right) $. $$ \left( \color{blue}{7x-8}\right) \cdot \left( 4x+2\right) = 28x^2+14x-32x-16 $$ |
| ② | Combine like terms: $$ 28x^2+ \color{blue}{14x} \color{blue}{-32x} -16 = 28x^2 \color{blue}{-18x} -16 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{28x^2-18x-16}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{28x^2-18x-16}\right) \cdot \left( x-5\right) = 28x^3-140x^2-18x^2+90x-16x+80 $$ |
| ④ | Combine like terms: $$ 28x^3 \color{blue}{-140x^2} \color{blue}{-18x^2} + \color{red}{90x} \color{red}{-16x} +80 = 28x^3 \color{blue}{-158x^2} + \color{red}{74x} +80 $$ |
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