Question

Разложите на множители
1)(x-y)+b(y-x)
2)2b(x-y)-(y-x)
3)a(b-c)+x(b-c)-7(b-c)
4)x(a-2)+y(2-a)-(2-a)
5)3(x+y)(x-y)-(x+y)^2
6)3m(n-m)^2-9m^2(m-n)

Answer 1

1)(x-y)+b(y-x)=-(y-x)+ b(y-x)= (y-x)(b-1)
2)2b(x-y)-(y-x)= 2b(x-y)+(x-y)= (x-y)(2b+1)
3)a(b-c)+x(b-c)-7(b-c)= (b-c)(a+x-7)
4)x(a-2)+y(2-a)-(2-a)= x(a-2)-y(a-2)+(a-2)= (a-2)(x-y+1)
5)3(x+y)(x-y)-(x+y)²=(x+y)(3(x-y)-(x+y))= (x+y)(3x-3y –x-y) = 2(x+y)(x-y)
6)3m(n-m)²-9m²(m-n)= (m-n)(3m(n-m)-9m²)= (m-n)( 3mn-3m²- 9m²)= 3m(m-n)( n-4m)