Question

1)x^5-x^3+X^21-1
2)a-b-a^2+b^2

Answer 1

$x^5-x^3+x^2-1=x^3(x^2-1)+1*(x^2-1)=(x^3+1)(x^2-1)=\\(x^3+1^3)(x^2-1^2)=\\(x+1)(x^2-x+1)(x+1)(x-1)=(x+1)^2(x^2+x+1)(x-1)$

$a-b-a^2+b^2=a-b-(a^2-b^2)=\\1*(a-b)-(a-b)(a+b)=(1-(a-b))(a+b)=(1-a+b)(a+b)$