https://file.aiquickdraw.com/mathbot/file/1727459754885cm7xvk41.jpg

In the image, you're asked to evaluate the expression:

\[
(3x + 2)(5x - 7)
\]

This is a binomial multiplication problem, so we will apply the distributive property (also known as FOIL for binomials). Let’s break it down:

1. Multiply the first terms: \( 3x \times 5x = 15x^2 \)
2. Multiply the outer terms: \( 3x \times -7 = -21x \)
3. Multiply the inner terms: \( 2 \times 5x = 10x \)
4. Multiply the last terms: \( 2 \times -7 = -14 \)

Now, combine the like terms:

\[
15x^2 - 21x + 10x - 14 = 15x^2 - 11x - 14
\]

So, the expression simplifies to:

\[
15x^2 - 11x - 14
\]

The correct answer is **Option D: \( 15x^2 - 11x - 14 \)**.

Would you like more details on how this is solved or have any other questions?

Here are 5 related questions:
1. How do you multiply more complex polynomials?
2. What is the distributive property and how is it applied in algebra?
3. What are some common mistakes when multiplying binomials?
4. How can you factor the result of this multiplication?
5. What is FOIL, and how is it used in polynomial multiplication?

**Tip:** When multiplying binomials, always ensure to combine like terms carefully to avoid mistakes in the final expression.

Learn how to multiply the binomials (3x + 2)(5x - 7) using the distributive property, commonly known as the FOIL method. This step-by-step solution covers key algebraic concepts and is suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation