Question
Answer
$$(3x+2)(2x+1)(x-5)=6x^3-23x^2-33x-10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x+2)(2x+1)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6x^2+3x+4x+2)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(6x^2+7x+2)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6x^3-30x^2+7x^2-35x+2x-10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6x^3-23x^2-33x-10\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x+2}\right) $ by each term in $ \left( 2x+1\right) $. $$ \left( \color{blue}{3x+2}\right) \cdot \left( 2x+1\right) = 6x^2+3x+4x+2 $$ |
| ② | Combine like terms: $$ 6x^2+ \color{blue}{3x} + \color{blue}{4x} +2 = 6x^2+ \color{blue}{7x} +2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{6x^2+7x+2}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{6x^2+7x+2}\right) \cdot \left( x-5\right) = 6x^3-30x^2+7x^2-35x+2x-10 $$ |
| ④ | Combine like terms: $$ 6x^3 \color{blue}{-30x^2} + \color{blue}{7x^2} \color{red}{-35x} + \color{red}{2x} -10 = 6x^3 \color{blue}{-23x^2} \color{red}{-33x} -10 $$ |
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