Question
Answer
$$(x-4)(x-1)(2x+1)=2x^3-9x^2+3x+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-4)(x-1)(2x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-x-4x+4)(2x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-5x+4)(2x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+x^2-10x^2-5x+8x+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3-9x^2+3x+4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-4}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{x-4}\right) \cdot \left( x-1\right) = x^2-x-4x+4 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-x} \color{blue}{-4x} +4 = x^2 \color{blue}{-5x} +4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-5x+4}\right) $ by each term in $ \left( 2x+1\right) $. $$ \left( \color{blue}{x^2-5x+4}\right) \cdot \left( 2x+1\right) = 2x^3+x^2-10x^2-5x+8x+4 $$ |
| ④ | Combine like terms: $$ 2x^3+ \color{blue}{x^2} \color{blue}{-10x^2} \color{red}{-5x} + \color{red}{8x} +4 = 2x^3 \color{blue}{-9x^2} + \color{red}{3x} +4 $$ |
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