How to Perform Operations on Functions (Subtraction). Algebra of Composite Functions (MATH 1010)
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The problem: Find (f - g)(x)
if f(x)=(6p+q)(5p-2q) and
g(x)=(p + 3q)^2
The solution: 29p^2 - 13pq - 11q^2
For both f(x) and g(x), we will want to expand the polynomials by using FOIL or area models for f(x) and we can use the square of a binomial property to expand g(x).
After we have done this, we write the two functions, subtracting g(x) which changes the signs of all three terms.
Then we combine like terms to complete the simplification process.