Question
Answer
$$(x+4)(2x+3)(x-1)=2x^3+9x^2+x-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+4)(2x+3)(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2+3x+8x+12)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2+11x+12)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3-2x^2+11x^2-11x+12x-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3+9x^2+x-12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+4}\right) $ by each term in $ \left( 2x+3\right) $. $$ \left( \color{blue}{x+4}\right) \cdot \left( 2x+3\right) = 2x^2+3x+8x+12 $$ |
| ② | Combine like terms: $$ 2x^2+ \color{blue}{3x} + \color{blue}{8x} +12 = 2x^2+ \color{blue}{11x} +12 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2+11x+12}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{2x^2+11x+12}\right) \cdot \left( x-1\right) = 2x^3-2x^2+11x^2-11x+12x-12 $$ |
| ④ | Combine like terms: $$ 2x^3 \color{blue}{-2x^2} + \color{blue}{11x^2} \color{red}{-11x} + \color{red}{12x} -12 = 2x^3+ \color{blue}{9x^2} + \color{red}{x} -12 $$ |
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