Find each product. See Example 5. (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.
4. Apply the difference of squares formula: $(2m{)}^2-(3{)}^2$.
5. Simplify the expression to get $4m^2-9$.

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 given 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 a² - b² = (a + b)(a - b). This identity is particularly useful when multiplying two binomials that are structured as a sum and a difference of the same terms, such as (2m + 3) and (2m - 3), allowing for a straightforward calculation of their product.

Binomial Multiplication

Binomial multiplication involves multiplying two binomials, which are algebraic expressions containing two terms. The process can be executed using the distributive property or special products like the difference of squares. Understanding how to apply these methods is crucial for accurately calculating the product of the given binomials.