4: =x^3+6x^2+12x+8-x(x^2-16)
=x^3+6x^2+12x+8-x^3+16x
=6x^2+28x+8
5: =x^3+8-x^3+8
=16
6: =27-27x^2+9x-x^3-(x^3+27)
=-x^3+9x-27x^2+27-x^3-27
=-2x^3-27x^2+9x
`a, (x+2)^3 - x(x-4)(x+4)`
`= x^3 + 6x^2 + 12x + 8 - x^3 + 16x`
`= 6x^2 + 28x + 8`
`b, (x+2)(x^2-2x+4)-(x^3-8)`
`= x^3 + 8 - x^3 + 8`
`= 16`.
`c, (3-x)^3 - (x+3)(x^2-3x+9)`
`= 27 - 27x + 9x^2-x^3 - x^3 - 27`
`= -2x^3 + 9x^2 - 27x`.
4) \(\left(x+2\right)^3-x\left(x-4\right)\left(x+4\right)\)
\(=\left(x^3+6x^2+12x+8\right)-x\left(x^2-16\right)\)
\(=x^2+6x^2+12x+8-x^3+16x\)
\(=6x^2+28x+8\)
5) \(\left(x+2\right)\left(x^2-2x+4\right)-\left(x^3-8\right)\)
\(=\left(x^3+8\right)-\left(x^3-8\right)\)
\(=x^3+8-x^3+8\)
\(=16\)
6) \(\left(3-x\right)^3-\left(x+3\right)\left(x^2-3x+9\right)\)
\(=27-9x^2+27x-x^3-x^3-27\)
\(=-2x^3-2x^2+9x\)
