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

2 (x^3 - x^2 + 2 x + 1)

Step-by-step explanation:

Simplify the following:

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

Factor -1 out of -3 x^3 + 2 x^2 + 1:

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

(-1)^2 = 1:

3 x^3 - 2 x^2 - 1 - x^3 + 4 x + 3

Grouping like terms, 3 x^3 - x^3 - 2 x^2 + 4 x - 1 + 3 = (-x^3 + 3 x^3) - 2 x^2 + 4 x + (3 - 1):

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

3 x^3 - x^3 = 2 x^3:

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

3 - 1 = 2:

2 x^3 - 2 x^2 + 4 x + 2

Factor 2 out of 2 x^3 - 2 x^2 + 4 x + 2:

2 (x^3 - x^2 + 2 x + 1)

Step-by-step explanation:

4x - x^3 + 3 - 2x^2 + 3x^3 - 1

2x^3 - 2x^2 + 4x + 2 is the solution