Question
Answer
$$(7x-8)(2x+3)(x-5)=14x^3-65x^2-49x+120$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7x-8)(2x+3)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(14x^2+21x-16x-24)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(14x^2+5x-24)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}14x^3-70x^2+5x^2-25x-24x+120 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}14x^3-65x^2-49x+120\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{7x-8}\right) $ by each term in $ \left( 2x+3\right) $. $$ \left( \color{blue}{7x-8}\right) \cdot \left( 2x+3\right) = 14x^2+21x-16x-24 $$ |
| ② | Combine like terms: $$ 14x^2+ \color{blue}{21x} \color{blue}{-16x} -24 = 14x^2+ \color{blue}{5x} -24 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{14x^2+5x-24}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{14x^2+5x-24}\right) \cdot \left( x-5\right) = 14x^3-70x^2+5x^2-25x-24x+120 $$ |
| ④ | Combine like terms: $$ 14x^3 \color{blue}{-70x^2} + \color{blue}{5x^2} \color{red}{-25x} \color{red}{-24x} +120 = 14x^3 \color{blue}{-65x^2} \color{red}{-49x} +120 $$ |
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