Question
Answer
$$(x-3)(x-4)(x-2)=x^3-9x^2+26x-24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-3)(x-4)(x-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-4x-3x+12)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-7x+12)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-2x^2-7x^2+14x+12x-24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-9x^2+26x-24\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-3}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x-3}\right) \cdot \left( x-4\right) = x^2-4x-3x+12 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-4x} \color{blue}{-3x} +12 = x^2 \color{blue}{-7x} +12 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-7x+12}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x^2-7x+12}\right) \cdot \left( x-2\right) = x^3-2x^2-7x^2+14x+12x-24 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-2x^2} \color{blue}{-7x^2} + \color{red}{14x} + \color{red}{12x} -24 = x^3 \color{blue}{-9x^2} + \color{red}{26x} -24 $$ |
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