Question

(x-3)^3-(x-3)(x^2+3x+9)+6(x+1)^2
x(x-4)(x+4)-(2-x)^3+2x^2
 

Answer 1

`a, = x^3 - 9x^2 + 27x - 27 - x^3 + 27 + 6x^2 + 12x + 6`

`= -3x^2 + 39 x + 6`

`= -3(x^2 - 13x -2)`

`b, = x^3 - 16x - 8 + 12x - 6x^2 + x^3+ 2x^2`

`= 2x^3 - 4x^2 - 4x - 8`

`= 2(x^3 - 4x^2 - 2x - 4)`

 

Answer 2

\(a,=x^3-9x^2+27x-27-x^3+27+6\left(x^2+2x+1\right)=-9x^2+27x+6x^2+12x+6=-3x^2+39x+6\\ b,=x\left(x^2-16\right)-\left(8-12x+6x^2-x^3\right)+2x^2=x^2-16x-8+12x-6x^2+x^3+2x^2=x^3-3x^2-4x-8\)

Answer 3

a: \(=x^3-9x^2+27x-27-x^3+27+6\left(x+1\right)^2\)

\(=-9x^2+27x+6x^2+12x+6\)

\(=-3x^2+39x+6\)

b: \(=x\left(x^2-16\right)+x^3-6x^2+12x-8+2x^2\)

\(=x^3-16x+x^3-4x^2+12x-8\)

\(=2x^3-4x^2+4x-8\)

Answer 4

\(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2=x^3-9x^2+27x-27-\left(x^3-27\right)+6\left(x^2+2x+1\right)=x^3+9x^2+27x-27-x^3+27+6x^2+12x+6=-3x^2+39x+6\)

\(x\left(x-4\right)\left(x+4\right)-\left(2-x\right)^3+2x^2=x\left(x^2-16\right)-\left(8-12x+6x^2-x^3\right)+2x^2=x^3-16x-8+12x-6x^2+x^3+2x^2=2x^3-4x-8-4x^2=2x^3-4x^2-4x-8\)