Use the FOIL method to multiply the binomials. (2xy+1)(3xy-2)

To multiply the binomials \((2xy + 1)(3xy - 2)\) using the FOIL method, we proceed as follows:

1. **First:** Multiply the first terms of each binomial.
   \[
   2xy \times 3xy = 6x^2y^2
   \]

2. **Outer:** Multiply the outer terms of the binomials.
   \[
   2xy \times -2 = -4xy
   \]

3. **Inner:** Multiply the inner terms of the binomials.
   \[
   1 \times 3xy = 3xy
   \]

4. **Last:** Multiply the last terms of each binomial.
   \[
   1 \times -2 = -2
   \]

Now, combine all these results:
\[
6x^2y^2 - 4xy + 3xy - 2
\]

Next, combine the like terms \(-4xy + 3xy\):
\[
6x^2y^2 - xy - 2
\]

So, the product of \((2xy + 1)(3xy - 2)\) is:
\[
\boxed{6x^2y^2 - xy - 2}
\]

Would you like any additional details, or do you have any questions?

Here are 5 related questions:
1. How would the FOIL method change if the signs inside the binomials were different?
2. What is the result of multiplying \((x + 2)(x - 2)\) using the FOIL method?
3. Can the FOIL method be applied to polynomials with more than two terms? Why or why not?
4. How do you multiply binomials with exponents using the FOIL method?
5. What happens if you multiply a binomial by a trinomial?

**Tip:** When combining like terms, always pay attention to the signs in front of each term to avoid mistakes.

Learn how to multiply binomials (2xy+1)(3xy-2) using the FOIL method with a detailed step-by-step solution. This problem covers key algebraic concepts including binomial multiplication and the FOIL method. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation