Question
Answer
$$(x-4)(x-3)(x-2)(x+4)=x^4-5x^3-10x^2+80x-96$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-4)(x-3)(x-2)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-3x-4x+12)(x-2)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-7x+12)(x-2)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3-2x^2-7x^2+14x+12x-24)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3-9x^2+26x-24)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4-5x^3-10x^2+80x-96\end{aligned} $$ | |
| 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: $$ x^2 \color{blue}{-3x} \color{blue}{-4x} +12 = x^2 \color{blue}{-7x} +12 $$ |
| 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: $$ x^3 \color{blue}{-2x^2} \color{blue}{-7x^2} + \color{red}{14x} + \color{red}{12x} -24 = x^3 \color{blue}{-9x^2} + \color{red}{26x} -24 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3-9x^2+26x-24}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x^3-9x^2+26x-24}\right) \cdot \left( x+4\right) = x^4+4x^3-9x^3-36x^2+26x^2+104x-24x-96 $$ |
| ⑥ | Combine like terms: $$ x^4+ \color{blue}{4x^3} \color{blue}{-9x^3} \color{red}{-36x^2} + \color{red}{26x^2} + \color{green}{104x} \color{green}{-24x} -96 = x^4 \color{blue}{-5x^3} \color{red}{-10x^2} + \color{green}{80x} -96 $$ |
This page was created using
Simplify polynomials calculator