Question
Answer
$$(3x+1)(4x-1)(x+3)=12x^3+37x^2+2x-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x+1)(4x-1)(x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(12x^2-3x+4x-1)(x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(12x^2+x-1)(x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}12x^3+36x^2+x^2+3x-x-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}12x^3+37x^2+2x-3\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x+1}\right) $ by each term in $ \left( 4x-1\right) $. $$ \left( \color{blue}{3x+1}\right) \cdot \left( 4x-1\right) = 12x^2-3x+4x-1 $$ |
| ② | Combine like terms: $$ 12x^2 \color{blue}{-3x} + \color{blue}{4x} -1 = 12x^2+ \color{blue}{x} -1 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{12x^2+x-1}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{12x^2+x-1}\right) \cdot \left( x+3\right) = 12x^3+36x^2+x^2+3x-x-3 $$ |
| ④ | Combine like terms: $$ 12x^3+ \color{blue}{36x^2} + \color{blue}{x^2} + \color{red}{3x} \color{red}{-x} -3 = 12x^3+ \color{blue}{37x^2} + \color{red}{2x} -3 $$ |
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