Step-by-step explanation:
Lets start with Left hand side
x^5 - y^5
To factor this we apply a formula
[tex]x^n−y^n=(x-y)(x^{n-1}+x^{n-2}y+x^{n-3}y^2...+xy^{n-2}+y^{n-1})[/tex]
Here n = 5
[tex](x-y)(x^{5-1}+x^{5-2}y+x^{5-3}y^2+x^{5-4}y^3+x^{5-5}y^4)[/tex]
now we simplify it
[tex](x-y)(x^4+x^3 y+x^2y^2+x^1y^3+x^0y^4)[/tex]
[tex](x-y)(x^4+x^3 y+x^2y^2+xy^3+y^4)[/tex]
We got the right hand side
[tex]x^5 - y^5 = (x-y)(x^4+x^3 y+x^2y^2+xy^3+y^4)[/tex]
