Find each product. (2m+3)(2m-3)

Verified step by step guidance

1. Recognize that the expression (2m+3)(2m-3) is a product of two binomials in the form (a+b)(a-b), which is a difference of squares pattern.
2. Recall the difference of squares formula: \(\\(a+b)(a-b) = a^2 - b^2\\)\).
3. Identify \(a = 2m\) and \(b = 3\) from the given binomials.
4. Apply the formula by squaring each term: calculate \(\left(2m\right)^2\) and \$3^2$ separately.
5. Write the product as \(\left(2m\right)^2 - 3^2\), which simplifies to \$4m^2 - 9$.

Key Concepts

Distributive Property

The distributive property allows you to multiply each term inside one parenthesis by each term inside the other. It is essential for expanding expressions like (2m + 3)(2m - 3) by multiplying 2m by both terms in the second parenthesis and then 3 by both terms.

Difference of Squares

The expression (a + b)(a - b) is a special product called the difference of squares, which simplifies to a² - b². Recognizing this pattern helps quickly find the product without full expansion, such as (2m + 3)(2m - 3) = (2m)² - 3².

Combining Like Terms

After expanding an expression, combining like terms means adding or subtracting terms with the same variable and exponent. This step simplifies the expression to its simplest form, making it easier to interpret or use in further calculations.