Question

Разложите на множители:
1)a^2-b^2-a+b=
2)a^3+a^2b-ab^2-b^3=
3)m^2+2mn+n^2-mb-nb=
4)xc-yc-x^2+2xy-y^2=

Answer 1

1)a^2-b^2-a+b=(a-b)(a+b)-(a-b)=(a-b)(a+b-1)
2)a^3+a^2b-ab^2-b^3=(a-b)(a^2+b^2+ab)+ab(a-b)=(a-b)(a^2+b^2+ab+ab)=(a-b)(a^2+b^2+2ab)
3)m^2+2mn+n^2-mb-nb=(m+n)^2-b(m+n)=(m+n)(m+n-b)
4)xc-yc-x^2+2xy-y^2=c(x-y)-(x-y)^2=(x-y)(c-x+y)