Разложите ** множители: а) (a-x)(x^2-y^2)-(x-y)(a^2-x^2) б) (a-x)(x^3-y^3)-(x-y)(a^3-x^3)

Question

Разложите на множители:

а) (a-x)(x^2-y^2)-(x-y)(a^2-x^2)

б) (a-x)(x^3-y^3)-(x-y)(a^3-x^3)

Answer 1

a) (a-x)(x-y)(x+y) - (x-y)(a-x)(a+x) = (a-x)(x-y)(x+y-a-x) = (a-x)(x-y)(y-a)
б) (a-x)(x-y)(x^2+xy+y^2) - (x-y)(a-x)(a^2+ax+x^2) = (a-x)(x-y)(x^2+xy+y^2-a^2-ax-x^2)= (a-x)(x-y)(xy+y^2-a^2-ax)