Question

ПОМОГИТЕ (2х+у)^3+(x-2y)^3=? (2mn-1)^3+1=? a^2+4b^2-9c^2-4ab=? x^3+x^2-xy^2-y^2=?

Answer 1

1) 
a³ + b³ = (a+b)(a² -ab+b²)
a=2x+y
b=x-2y
(2x+y)³ + (x-2y)³=(2x+y+x-2y)((2x+y)² -(2x+y)(x-2y)+(x-2y)²)=
=(3x-y)(4x²+4xy+y² -(2x³+xy-4xy-2y²)+x² -4xy+4y²)=
=(3x-y)(4x² +4xy+y² -2x³ +3xy +2y² +x² -4xy+4y²)=
=(3x-y)(5x² -2x³ +7y² +3xy)=15x³-5x²y-6x⁴+2x³y+21xy²-7y³+9x²y-3xy²=
=15x³ -6x⁴ -7y³ +2x³y+4x²y+18xy²

2)
(2mn-1)³ +1³ =(2mn-1+1)((2mn-1)² -(2mn-1)*1+1²)=
=2mn(4m²n²-4mn+1-2mn+1+1)=2mn(4m²n²-6mn+3)=8m³n³-12m²n²+6mn

3)
a²+4b² -9c² -4ab=(a² -4ab+4b²)-9c² =(a-2b)² -9c² =(a-2b-3c)(a-2b+3c)

4)
x³ +x² -xy² -y² =(x³ +x²)-(xy² +y²)=x²(x+1)-y²(x+1)=(x+1)(x² -y²)=
=(x+1)(x-y)(x+y)