Question

Find the product. Simplify your answer.
(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:
\[
\boxed{f^2 + 4f + 3}
\]