1. The problem is to find the expanded form of the function $f(x) = (x-2)(x+3)$. 2. We use the distributive property (also known as FOIL for binomials) which states: $$ (a+b)(c+d) = ac + ad + bc + bd $$ 3. Applying FOIL to $f(x)$: $$ (x-2)(x+3) = x \cdot x + x \cdot 3 - 2 \cdot x - 2 \cdot 3 $$ 4. Simplify each term: $$ = x^2 + 3x - 2x - 6 $$ 5. Combine like terms: $$ = x^2 + \cancel{3x - 2x} + (-6) = x^2 + x - 6 $$ 6. Therefore, the expanded form of $f(x)$ is: $$ f(x) = x^2 + x - 6 $$