Question
Answer
$$(x-4)(x+3)(x-5)=x^3-6x^2-7x+60$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-4)(x+3)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+3x-4x-12)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-x-12)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-5x^2-x^2+5x-12x+60 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-6x^2-7x+60\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-4}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x-4}\right) \cdot \left( x+3\right) = x^2+3x-4x-12 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{3x} \color{blue}{-4x} -12 = x^2 \color{blue}{-x} -12 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-x-12}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x^2-x-12}\right) \cdot \left( x-5\right) = x^3-5x^2-x^2+5x-12x+60 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-5x^2} \color{blue}{-x^2} + \color{red}{5x} \color{red}{-12x} +60 = x^3 \color{blue}{-6x^2} \color{red}{-7x} +60 $$ |
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