Question
Answer
$$(3-x)\cdot(4-x)\cdot(5-x)=-x^3+12x^2-47x+60$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3-x)\cdot(4-x)\cdot(5-x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(12-3x-4x+x^2)\cdot(5-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-7x+12)\cdot(5-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5x^2-x^3-35x+7x^2+60-12x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-x^3+12x^2-47x+60\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3-x}\right) $ by each term in $ \left( 4-x\right) $. $$ \left( \color{blue}{3-x}\right) \cdot \left( 4-x\right) = 12-3x-4x+x^2 $$ |
| ② | Combine like terms: $$ 12 \color{blue}{-3x} \color{blue}{-4x} +x^2 = x^2 \color{blue}{-7x} +12 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-7x+12}\right) $ by each term in $ \left( 5-x\right) $. $$ \left( \color{blue}{x^2-7x+12}\right) \cdot \left( 5-x\right) = 5x^2-x^3-35x+7x^2+60-12x $$ |
| ④ | Combine like terms: $$ \color{blue}{5x^2} -x^3 \color{red}{-35x} + \color{blue}{7x^2} +60 \color{red}{-12x} = -x^3+ \color{blue}{12x^2} \color{red}{-47x} +60 $$ |
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