Question

g(x) = x² + 3x
f(x) = x + 3
find g(x) · f(x)

Explanation:

Step1: Substitute given functions

$g(x) \cdot f(x) = (x^2 + 3x)(x + 3)$

Step2: Distribute terms via FOIL

$= x^2(x) + x^2(3) + 3x(x) + 3x(3)$

Step3: Calculate each product

$= x^3 + 3x^2 + 3x^2 + 9x$

Step4: Combine like terms

$= x^3 + (3x^2 + 3x^2) + 9x$

Answer:

$x^3 + 6x^2 + 9x$