To solve this problem, we must understand function notation and the operations that go along with it. For Example, in this problem, f(x)g(x) means that we must multiply f(x) by g(x). What this means is we should multiply the functions by one another, as modeled below:
f(x)g(x)
(3x^2 + 5x)(7x +3)
To simplify this expression, we must use the FOIL method for multiplying binomials, which means we multiply together the first, outer, inner, and last terms and then add them together. This is modeled below:
(3x^2)(7x) + (5x)(7x) + (3x^2)(3) + (5x)(3)
To simplify this expression, we must first perform the multiplication within each term:
21x^3 + 35x^2 + 9x^2 + 15x
Next, we can add together the two terms with the same exponents:
21x^3 + 44x^2 + 15x
Therefore, your answer is 21x^3 + 44x^2 + 15x.
Hope this helps!
