Question
Answer
$$(x-1)(3x-1)(4x+5)=12x^3-x^2-16x+5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-1)(3x-1)(4x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3x^2-x-3x+1)(4x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(3x^2-4x+1)(4x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}12x^3+15x^2-16x^2-20x+4x+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}12x^3-x^2-16x+5\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( 3x-1\right) $. $$ \left( \color{blue}{x-1}\right) \cdot \left( 3x-1\right) = 3x^2-x-3x+1 $$ |
| ② | Combine like terms: $$ 3x^2 \color{blue}{-x} \color{blue}{-3x} +1 = 3x^2 \color{blue}{-4x} +1 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{3x^2-4x+1}\right) $ by each term in $ \left( 4x+5\right) $. $$ \left( \color{blue}{3x^2-4x+1}\right) \cdot \left( 4x+5\right) = 12x^3+15x^2-16x^2-20x+4x+5 $$ |
| ④ | Combine like terms: $$ 12x^3+ \color{blue}{15x^2} \color{blue}{-16x^2} \color{red}{-20x} + \color{red}{4x} +5 = 12x^3 \color{blue}{-x^2} \color{red}{-16x} +5 $$ |
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