Mister Exam

# Factor polynomial a^5-b^5

An expression to simplify:

### The solution

You have entered [src]
 5    5
a  - b 
$$a^{5} - b^{5}$$
a^5 - b^5
Factorization [src]
        /      /                     ___________\\ /      /                     ___________\\ /      /                     ___________\\ /      /                     ___________\\
|      |        ___         /       ___ || |      |        ___         /       ___ || |      |        ___         /       ___ || |      |        ___         /       ___ ||
|      |  1   \/ 5         /  5   \/ 5  || |      |  1   \/ 5         /  5   \/ 5  || |      |  1   \/ 5         /  5   \/ 5  || |      |  1   \/ 5         /  5   \/ 5  ||
(a - b)*|a - b*|- - + ----- - I*  /   - + ----- ||*|a - b*|- - + ----- + I*  /   - + ----- ||*|a - b*|- - - ----- - I*  /   - - ----- ||*|a - b*|- - - ----- + I*  /   - - ----- ||
\      \  4     4       \/    8     8   // \      \  4     4       \/    8     8   // \      \  4     4       \/    8     8   // \      \  4     4       \/    8     8   //
$$\left(a - b\right) \left(a - b \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(a - b \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(a - b \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(a - b \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right)$$
((((a - b)*(a - b*(-1/4 + sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8))))*(a - b*(-1/4 + sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8))))*(a - b*(-1/4 - sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8))))*(a - b*(-1/4 - sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))
Numerical answer [src]
a^5 - b^5
a^5 - b^5
Combinatorics [src]
        / 4    4      3      3    2  2\
(a - b)*\a  + b  + a*b  + b*a  + a *b /
$$\left(a - b\right) \left(a^{4} + a^{3} b + a^{2} b^{2} + a b^{3} + b^{4}\right)$$
(a - b)*(a^4 + b^4 + a*b^3 + b*a^3 + a^2*b^2)
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