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 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 expression.
4. Apply the formula by squaring \(a\) and \(b\): calculate \((2m)^2\) and \(3^2\).
5. Write the product as \((2m)^2 - 3^2\), which simplifies to \(4m^2 - 9\).

Key Concepts

Difference of Squares

The difference of squares is a special product formula: (a + b)(a - b) = a² - b². It simplifies the multiplication of two binomials where one is the sum and the other is the difference of the same terms, resulting in the subtraction of their squares.

Binomial Multiplication

Multiplying binomials involves applying the distributive property (FOIL method) to combine each term in the first binomial with each term in the second. This process expands the expression into a polynomial.

Polynomial Simplification

After multiplying, like terms must be combined to simplify the expression into its simplest polynomial form. This step ensures the final answer is concise and correctly represents the product.