Find each product. See Examples 5 and 6. (2m+3)(2m-3)

Verified step by step guidance

1. Recognize that the expression (2m+3)(2m-3) is a difference of squares.
2. Recall the formula for the difference of squares: (a+b)(a-b) = a^2 - b^2.
3. Identify a = 2m and b = 3 in the expression (2m+3)(2m-3).
4. Apply the difference of squares formula: (2m)^2 - 3^2.
5. Simplify the expression: calculate (2m)^2 and 3^2 separately, then subtract the results.

Key Concepts

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In the context of the question, recognizing that (2m+3) and (2m-3) are binomials that can be multiplied using the difference of squares formula is essential for finding the product.

Difference of Squares

The difference of squares is a specific algebraic identity that states that the product of two binomials in the form (a+b)(a-b) equals a² - b². This concept is crucial for simplifying the expression (2m+3)(2m-3) into a more manageable form, as it allows us to directly apply the identity to find the product.

Binomial Multiplication

Binomial multiplication involves multiplying two binomials, which are algebraic expressions containing two terms. Understanding how to distribute each term in one binomial to every term in the other is key to finding the product. In this case, applying the distributive property will help in calculating the final result of (2m+3)(2m-3).