Find the product. Simplify your answer.

Question

(4b+1)(3b+1)

Answer 1

To find the product of the expressions \((4b + 1)(3b + 1)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Multiply the first terms: \[ 4b \cdot 3b = 12b^2 \]

2. Multiply the outer terms: \[ 4b \cdot 1 = 4b \]

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

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

Now, combine all these results: \[ 12b^2 + 4b + 3b + 1 \]

Combine like terms (\(4b + 3b\)): \[ 12b^2 + 7b + 1 \]

Thus, the simplified product is: \[ \boxed{12b^2 + 7b + 1} \]