Тест5. Сумма и разность кубов 2-ух вырожения. Внедрения разных способов

1.

1) 1000m^3-n^3=(10m)^3-n^3= (10m-n)(100m^2+10mn+n^2)

2) 81a^3-ab^2=a(81a^2-b^2)=a(9a-b)(9a+b)

3) -8x^2-16xy-8y^2= -8(x^2+2xy+y^2)=-2(x+y)^2= -8(x+y)(x+y)

4) 5mn-10n+15m-30=5m(x+3)-10n(n+3)=(n+3)(5m-10n)=5(n+3)(m-2n)

3.

1) a^2-36b^2+a-6b=(a-6b)(a+6b) +(a-6b)= (a-6b)(a+6b+1)

2)25x^2-10xy+y^2-9=(5x-y)^2-9=(5x-y-3)(5x-y+3)

3) ay^7+y^7-ay^3-y^3=y^7(a+1)-y^3(a+1)=(a+1)(y^7-y^3)

4) 4-m^2+14mn-49n^2=4-(m^2-14mn+49m^2)=4-(m-7n)^2=

= [2-(m-7n)][ 2+(m-7n)]=(2-m-7n)(2+m-7n)

4.

1) 2x^2-32x=0

2x(x^2-16)=0

2x=0 , x-4=0 , x+4=0

X1=0 x2=4 x3=-4

2) 81x^3+18x^2+x=0

X(81x^2+18x+1)=0

X(x+1/9)(x+1/9)=0

X1=0 , x+1/9=0

X2=-1/9

3) x^3+6x^2-x-6=0

X^2(x+6)-(x+6)=0

(x+6)(x^2-1)=0

(x+6)(x-1)(x+1)=0

X=6 , x-1=0 , x+1=0

X1=-6 x2=1 x3=-1