1.
1) m³+27n³=(m+3n)(m²-3mn+n²)
2) x³-64xy²=x(x²-64y²)=x(x-8y)(x+8y)
3) -3a²+18a-27=-3(a²-6+9)=-3(a-3)²
4) 2ab+10b-2a-10=2ab-2a+10b-10=2a(b-1)+10(b-1) (2a+10)(b-1)
5)a^4-16=a^4-2^4=(a-2)(a+2)(a²+4)
2.
(2a-1)(4a²+2a+1)=a³-1³=a³-1 , a=-1/2
-(1/2)³-1=-1/8-1=-1 1/8
3.
x²-y²+x-y=x²+x-y²-y=x(x+1)-y(y+1)
4x²-4xy+y²-9=(2x-y)²-9=(2x-y-3)(2x-y+3)
ac^4-c^4-ac²+c²=c^4(a-1)-c²(a-1)=(c^4-c²)(a-1)=c²(c²-1)(a-1)
4-m²+2mn-n²=-4+m²-2mn+n²=-4+(m-n)²=(m-n)²-4=(m-n-2)(m-n+2)
4.
1) 6x³-24x=0
6x(x²-4)=0
6x=0 x²-4=0
x1=0 x²=4
x2=2
x3=-2
2) 25x³-10x²+x=0
x(25x²-10x+1)=0
x1=0 25x²-10x+1=0
D=100-4*25*1=0
x2=10/(2*25)
x2=0.2
3) x³-4x² -9x+36=0
x²(x-4)-9(x-4)=0
(x²-9)(x-4)=0
x²-9=0 x-4=0
x²=9 x1=4
x2=3
x3=-3
5.
2^12+5³=4096+125=4221
4221:21=201
4200:21+21:21=200+1=201
6.
a+b=5 ab=-2 a=5-b
(a-b)²=a²-2ab+b²=a²+b²-2ab= (5-b)² -b²-2*(-2)=25-10b+b²-b²+4 =29-b