Additive inverse is the negative of the number, i.e. what you add to the number to get zero.
So the additive inverse of number b is - b
Additive inverse of 4 is - 4.
Then, you can verify the subtraction is the same that add the additive inverse.
For example subtracting 4 from 10 (10 - 4) is the same that adding -4:
10 - 4 = 10 + (-4).
Then given any expression if you have to subtract other expressión you just add the addive inverse of the second expression.
For example: given A(x) = x^2 + 3x + 5 and B(x) = 2x + 4
Find A(x) - B(x) = A(x) + [-B(x)]
=> x^2 + 3x + 5 + (-2x -4) = x^2 + 3x - 2x + 5 - 4 = x^2 + x + 1
