Question

5. Упростите выражение:
1) 6(х+1)2 + 2(x-1)(х2 +х+1) – 2(x + 1);
2) 5х(х – 3)2 – 5(х – 1)3 + 15(х + 2)(х – 2);
3) (x + 2)3 - x(3х + 1)2 + (2x+1)(4х2 – 2х + 1).​

Answer 1

$\displaystyle \tt 1) \: 6(x+1)^2+2(x-1)(x^2+x+1)-2(x+1)=6(x^2+2x+1)+2(x^3-1)-2x-2=6x^2+12x+6+2x^3-2-2x-2=6x^2+10x+2+2x^3=\boxed{\bold{2x^3+6x^2+10x+2}}$

$\displaystyle \tt 2) \: 5x(x-3)^2-5(x-1)^3+15(x+2)(x-2)=5x(x^3-6x+9)-5(x^3-3x^2+3x-1)+15(x^2-4)=5x^3-30x^2+45x-5x^3+15x^2-15x+5+15x^2-60=\boxed{\bold{30x-55}}$

$\displaystyle \tt 3) \: (x+2)^3-x(3x+1)^2+(2x+1)(4x^2-2x+1)=x^3+6x^2+12x+8-x(9x^2+6x+1)+8x^3+1=x^3+6x^x+12x+8-9x^3-6x^2-x+8x^3+1=\boxed{\bold{11x+9}}$