https://file.aiquickdraw.com/mathbot/file/1726253538508xwt5zhu2.jpg

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.

Learn how to multiply and simplify the binomial expression (2b - 3)(7b + 2) using the distributive property. This step-by-step solution covers key algebraic concepts and demonstrates how to simplify quadratic terms. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation