Algebra 2/trig question.?

Question

How do you factor (x to the fifth power) plus (y to the fifth power)?

Answer 1

How about starting with

(x^2 + y^2) * (x^2 - y*2)?

That's x^4 - y^4

Now let's throw in (x - y) and see what happens:

(x^4 - y^4) * (x - y) = x^5 + y^5 - x^4y - y^4x

Hopeless.

Answer 2

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Answer 3

x^5 + y^5 = (x + y)(x^4 - x^3y + x^2y^2 - xy^3 + y ^ 4)

The general form for factoring x^n - y^n is:

x^n - y^n = (x - y)( x^(n-1) + x^(n-2)y + ... + xy^(n-2) + y^(n - 1) )

For odd n, you can make the substitution y = -y and get the factors of x^n + y^n.

Answer 4

respect to y
(y+x)[(y^2+((sqrt5-1)yx)/2+x^2][(y^2+((sqrt5-1)yx)/2+x^2]

respect to x
(x+y)[(x^2+((sqrt5-1)xy)/2+y^2][(x^2+((sqrt5-1)xy)/2+y^2]

Answer 5

you cant