Разложите ** множители1)a^4+a^2+12)(x+y-z)^2-(x-y+z)^2

Question

Разложите на множители
1)a^4+a^2+1
2)(x+y-z)^2-(x-y+z)^2

Answer 1

A⁴+a²+1=(a⁴+2a²+1)-a²=
=(a²+1)²-a²=(a²+1+a)(a²+1-a)

(x+y-z)²-(x-y+z)²=
=((x+y-z) + (x-y+z)) ((x+y-z) -(x-y+z))= =(2x)*(2y-2z)=4x(y-z)