Докажите,что при любых значениях переменных значение выражения равно нулю:1)(a+x)^3-a(a+x)^2-x^2(2a+x)-a^2x.2)(a-1)^3+3(a-1)^2+3(a-1)+1-a^3.3)(x^3+y^3)^2-(x^2+y^2)^3+3x^2y^2(x+y)^2-8x^3y^3.4)(m-3n)^3-(2m-3n)(3mn+(m-3n)^2)+m^3
1) (a+x)³-a*(a+x)²-x²*(2a+x)-a²x=(a+x)²(a+x-a)+2ax²-a²x= =(a²+2ax+x²)*x-2ax²-x³-a²x=a²x+2ax²+x³-2ax²-x³-a²x=0. 2) (a-1)³+3*(a-1)²+3*(a-1)+1-a³=(a-1)²*(a-1+3)+3a-3+1-a³= =(a²-2a+1)*(a+2)+3a+-2-a³=a³-2a²+a+2a²-4a+2+3a-2-a³=0. 3) (x³+y³)²-(x²+y²)³+3x²y²*(x+y)²-8x³y³= =x⁶+2x³y³+y⁶-x⁶-3x⁴y²-3x²y⁴-y⁶+3x²y²*(x²+2xy+y²)-8x³y³= =2x³y³-3x⁴y²-3x²y⁴+3x⁴y²+6x³y³+3x²y⁴-8x³y³=0. 4) (m-3n)³-(2m-3n)(3mn+(m-3n)²)+m³= =m³-9m²n+27mn²-27n³-(2m-3n)*(3mn+m²-6mn+9n²)+m³= =m³-9m²n+27mn²-27n³- -(6m²n+2m³-12m²n+18mn²-9mn²-3m²n+18mn²-27n³)+m³= =2m³-9m²n+27mn²-27n³-(-9m²n+2m³+27mn²-27n³)= =2m³-9m²n+27mn²-27n³+9m²n-2m³-27mn²+27n³=0.