Mister Exam
Factor polynomial a^5-b^5
The solution
Factorization
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/ / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\
| | ___ / ___ || | | ___ / ___ || | | ___ / ___ || | | ___ / ___ ||
| | 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)))
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)