Let's simplify the expression $(3b + 2)(5b + 5)$ using the distributive property (also known as the FOIL method for binomials).

Step 1: Apply the distributive property.

$(3b + 2)(5b + 5) = 3b(5b) + 3b(5) + 2(5b) + 2(5)$

Step 2: Perform the multiplications.

$3b(5b) = 15b^2$ $3b(5) = 15b$ $2(5b) = 10b$ $2(5) = 10$

Step 3: Combine all the terms.

$15b^2 + 15b + 10b + 10$

Step 4: Combine like terms.

$15b^2 + (15b + 10b) + 10 = 15b^2 + 25b + 10$

Final answer:

$15b^2 + 25b + 10$

Would you like further details on any part of this process?

Here are 5 related questions to expand your understanding:

1. How does the distributive property work for multiplying binomials?
2. What is the FOIL method, and how is it applied?
3. How do you combine like terms when simplifying expressions?
4. What are like terms, and why is it important to group them?
5. Can this same method be applied to polynomials with more than two terms?

Tip: Always group like terms to simplify expressions as much as possible!