https://file.aiquickdraw.com/mathbot/file/1730141240206gm8nibmh.jpg

To solve the expression \((7x + 3)(4x - 5)\), we need to use the distributive property, often known as the FOIL method for binomials:

1. **First terms:** \(7x \cdot 4x = 28x^2\)
2. **Outer terms:** \(7x \cdot -5 = -35x\)
3. **Inner terms:** \(3 \cdot 4x = 12x\)
4. **Last terms:** \(3 \cdot -5 = -15\)

Now, combine the terms:

\[
28x^2 - 35x + 12x - 15
\]

Simplify by combining like terms:

\[
28x^2 - 23x - 15
\]

The correct answer is:
\[
\boxed{28x^2 - 23x - 15}
\]

Would you like further details or have any questions?

---

Here are some related questions to deepen understanding:

1. What is the FOIL method, and why is it useful for multiplying binomials?
2. How would the expression change if the signs of the constants in \((7x + 3)(4x - 5)\) were different?
3. Can this multiplication process be applied to expressions with more than two terms, like \((7x + 3 + 2y)(4x - 5 + y)\)?
4. How can this process help when simplifying expressions in polynomial long division?
5. What is the difference between expanding polynomials and factoring them?

**Tip:** Always double-check each term after distributing to avoid simple sign errors.

Multiply the polynomials: (7x + 3)(4x - 5)

Learn how to multiply the polynomials (7x + 3)(4x - 5) using the FOIL method. This problem covers key algebraic concepts and is 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