Question
Answer
$$(3x-5)(2x+1)(x-2)=6x^3-19x^2+9x+10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x-5)(2x+1)(x-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6x^2+3x-10x-5)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(6x^2-7x-5)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6x^3-12x^2-7x^2+14x-5x+10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6x^3-19x^2+9x+10\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x-5}\right) $ by each term in $ \left( 2x+1\right) $. $$ \left( \color{blue}{3x-5}\right) \cdot \left( 2x+1\right) = 6x^2+3x-10x-5 $$ |
| ② | Combine like terms: $$ 6x^2+ \color{blue}{3x} \color{blue}{-10x} -5 = 6x^2 \color{blue}{-7x} -5 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{6x^2-7x-5}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{6x^2-7x-5}\right) \cdot \left( x-2\right) = 6x^3-12x^2-7x^2+14x-5x+10 $$ |
| ④ | Combine like terms: $$ 6x^3 \color{blue}{-12x^2} \color{blue}{-7x^2} + \color{red}{14x} \color{red}{-5x} +10 = 6x^3 \color{blue}{-19x^2} + \color{red}{9x} +10 $$ |
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