Find the product. Simplify your answer.

Question

(f+1)(f+3)

Answer 1

To find the product of \((f+1)(f+3)\), we can use the distributive property (also known as the FOIL method for binomials).

1. First: Multiply the first terms:
   \[ f \cdot f = f^2 \]

2. Outer: Multiply the outer terms:
   \[ f \cdot 3 = 3f \]

3. Inner: Multiply the inner terms:
   \[ 1 \cdot f = f \]

4. Last: Multiply the last terms:
   \[ 1 \cdot 3 = 3 \]

Now, we can combine all these results:
\[ f^2 + 3f + f + 3 \]

Next, combine the \(3f\) and \(f\) terms:
\[ f^2 + 4f + 3 \]

So, the simplified product of \((f+1)(f+3)\) is:
\[ \boxed{f^2 + 4f + 3} \]