Question

Разложите на множители:
1) 3ab^3-3a^3b
2) 6u^2-54y^2
3) 3c(p+q)+p+q
4) 4p(m-3n)+3n-m
5) 2x(m+2n)-y(2n+m)
6) a^2+b^2+2ab+5a+5b
7) (0,1a-b)^2-(a+0,1b)^2

Answer 1

1) 3ab^3-3a^3b = 3ab(b^2-a^2) = 3ab(b-a)b+a)
2) 6u^2-54y^2 =  6(u^2-9y^2) = 6(u-y)(u+y)
3) 3c(p+q)+p+q= (p+q)(3c+1)
4) 4p(m-3n)+3n-m = (m-3n)(4p-1)
5) 2x(m+2n)-y(2n+m)=(m+2n)(2x-y)
6) a^2+b^2+2ab+5a+5b= (a+b)^2 + 5(a+b) = (a+b)(a+b+5)
7) (0,1a-b)^2-(a+0,1b)^2 = [(0,1a-b) - (a+0,1b)][(0,1a-b) + (a+0,1b)] =                  = (0,1a-b-a-0,1b)(0,1a-b+a+0,1b) = (-0,9-1,1b)(1,1a-0,9b)