How do you factor x⁵-y⁵?

We have to evaluate x5 – y5

Solution

We know the formula that

If n is a natural number, aⁿ – bⁿ = (a – b)(a^n-1 + a^n-2b+…+ b^n-2a + b^n-1)

So

x⁵ – y⁵= (x-y) (x^5-1 + x^5-2b + x^5-3y2+x^5-4y3+y4)

x⁵ – y⁵= (x-y) (x4 + x³b + x²y²+x¹y³+y⁴)