Question
Answer
$$(x-5)^4=x^4-20x^3+150x^2-500x+625$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-5)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4-20x^3+150x^2-500x+625\end{aligned} $$ | |
| ① | $$ (x-5)^4 = (x-5)^2 \cdot (x-5)^2 $$ |
| ② | Find $ \left(x-5\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 5 }$. $$ \begin{aligned}\left(x-5\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 5 + \color{red}{5^2} = x^2-10x+25\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-10x+25}\right) $ by each term in $ \left( x^2-10x+25\right) $. $$ \left( \color{blue}{x^2-10x+25}\right) \cdot \left( x^2-10x+25\right) = x^4-10x^3+25x^2-10x^3+100x^2-250x+25x^2-250x+625 $$ |
| ④ | Combine like terms: $$ x^4 \color{blue}{-10x^3} + \color{red}{25x^2} \color{blue}{-10x^3} + \color{green}{100x^2} \color{orange}{-250x} + \color{green}{25x^2} \color{orange}{-250x} +625 = \\ = x^4 \color{blue}{-20x^3} + \color{green}{150x^2} \color{orange}{-500x} +625 $$ |
This page was created using
Simplify polynomials calculator