Question
Answer
$$(x-1)(x-3)(x+3)-5=x^3-x^2-9x+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-1)(x-3)(x+3)-5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-3x-x+3)(x+3)-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-4x+3)(x+3)-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+3x^2-4x^2-12x+3x+9-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-x^2-9x+4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{x-1}\right) \cdot \left( x-3\right) = x^2-3x-x+3 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-3x} \color{blue}{-x} +3 = x^2 \color{blue}{-4x} +3 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-4x+3}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x^2-4x+3}\right) \cdot \left( x+3\right) = x^3+3x^2-4x^2-12x+3x+9 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{3x^2} \color{blue}{-4x^2} \color{red}{-12x} + \color{red}{3x} + \color{green}{9} \color{green}{-5} = x^3 \color{blue}{-x^2} \color{red}{-9x} + \color{green}{4} $$ |
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