Question

Разложите на множители 1) -5a^2-10ab-5b^2 2) (x-y)^2+3(x-y) 3) a^5-a^3+a^2-1 4) 25-9m^2+6mn-n^2

Answer 1

1) -5a^2-10ab-5b^2=-5(a^2+2ab+b^2)=-5(a+b)^2
2) (x-y)^2+3(x-y)=(x-y)(x-y+3)
3) a^5-a^3+a^2-1=a^3(a^2-1)+(a^2-1)=(a^2-1)(a^3+1)=(a-1)(a+1)(a+1)(a^2-a+1)=(a-1)(a^2-a+1)(a+1)^2

Answer 2

1) -5a^2-10ab-5b^2 = -5(a^2+2ab+b^2) = -5(a+b)^2

2) (x-y)^2+3(x-y) = (x-y)(x-y+3)

3) a^5-a^3+a^2-1 = a^5-a^3+a^2-1 = a^3(a^2-1) + (a^2-1) = (a^3+1)(a^2-1)

4) 25-9m^2+6mn-n^2 = (5-3m+n)(5+3m-n)