Addition and Subtraction of Polynomials

Since polynomials are algebraic expressions, when adding or subtracting polynomials, the resulting polynomial can be simplified by adding and subtracting like terms

Let \( \mathrm{P}(x) = Ax^3 + Bx^2 + Cx + D\) and \( \mathrm{Q}(x) = Ex + F\)
Then,
\( \mathrm{P}(x) + \mathrm{Q}(x) = Ax^3 + Bx^2 + (C + E)x + (D + F) \)

Let \( \mathrm{P}(x) = 4x^5 + 3x^3 - 12x + 7\) and \( \mathrm{Q}(x) = 4x^3 - 3x^2 \)
Find \( \mathrm{P}(x) - \mathrm{Q}(x) \)