а) (2а^3-3b^2)^2-(2a^3+b^2)^2=(2a³-3b²+2a³+b²)(2a³-3b²-2a³-b²)=(4a³-2b²)(-4b²)=-8b²(2a³-b²)
б) x^2-5x+4=x²-x-4x+4=x(x-1)-4(x-1)=(x-1)(x-4)
в) 1/4a^4+2a^2b^2+4b^4=(a²/2+2b²)(a²/2+2b²)
г) x^2+6xy+8y^2=x²+4xy+2xy+8y²=x(x+4y)+2y(x+4y)=(x+4y)(x+2y)
3(3-x^2)-(9-3x^2+x^4)(x^2+3)-3(x^2-x)(x^2+x)=
9-3x²-x⁶-27-3(x⁴-x²)=9-3x²-x⁶-27-3x⁴+3x²=-x⁶-3x⁴-18
(x-1)(x-3)(x+4)-(x+1)(x+3)(x-4)=
(x-1)(x²-3x+4x-12)-(x+1)(x²+3x-4x-12)=
(x-1)(x²+x-12)-(x+1)(x²-x-12)=
x³-x²+x²-x-12x+12-(x³+x²-x²-x-12x-12)=
x³-13x+12-x³+13x+12=24
а) (2а^3-3b^2)^2-(2a^3+b^2)^2=(2a³-3b²+2a³+b²)(2a³-3b²-2a³-b²)=(4a³-2b²)(-4b²)=-8b²(2a³-b²)
б) x^2-5x+4=x²-x-4x+4=x(x-1)-4(x-1)=(x-1)(x-4)
в) 1/4a^4+2a^2b^2+4b^4=(a²/2+2b²)(a²/2+2b²)
г) x^2+6xy+8y^2=x²+4xy+2xy+8y²=x(x+4y)+2y(x+4y)=(x+4y)(x+2y)
3(3-x^2)-(9-3x^2+x^4)(x^2+3)-3(x^2-x)(x^2+x)=
9-3x²-x⁶-27-3(x⁴-x²)=9-3x²-x⁶-27-3x⁴+3x²=-x⁶-3x⁴-18
(x-1)(x-3)(x+4)-(x+1)(x+3)(x-4)=
(x-1)(x²-3x+4x-12)-(x+1)(x²+3x-4x-12)=
(x-1)(x²+x-12)-(x+1)(x²-x-12)=
x³-x²+x²-x-12x+12-(x³+x²-x²-x-12x-12)=
x³-13x+12-x³+13x+12=24