To solve the expression $(2b - 3)(7b + 2)$, we will apply the distributive property (also known as FOIL for binomials).

Step-by-step solution:

$(2b - 3)(7b + 2)$

1. Multiply the first terms: $2b \times 7b = 14b^2$

2. Multiply the outer terms: $2b \times 2 = 4b$

3. Multiply the inner terms: $-3 \times 7b = -21b$

4. Multiply the last terms: $-3 \times 2 = -6$

Combine all the terms:

$14b^2 + 4b - 21b - 6$

Simplify by combining like terms:

$14b^2 - 17b - 6$

Thus, the simplified expression is: $\boxed{14b^2 - 17b - 6}$

Would you like further details or have any questions?

Here are 5 follow-up questions that expand on this problem:

1. How would you factor a quadratic like $14b^2 - 17b - 6$?
2. What is the difference between the FOIL method and the distributive property for binomials?
3. Can you solve for $b$ if $14b^2 - 17b - 6 = 0$?
4. How would this multiplication change if we added more terms to the binomials (e.g., trinomials)?
5. What is the geometric representation of multiplying two binomials?

Tip: Always simplify your expression by combining like terms to make the final answer more readable.