Find each product. See Example 5. (2m + 3) (2m - 3)

Guida verificata passo dopo passo

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.

Recall the difference of squares formula: \((a + b)(a - b) = a^2 - b^2\).

Identify \(a = 2m\) and \(b = 3\) from the given expression.

Apply the formula by squaring \(a\) and \(b\): calculate \((2m)^2\) and \(3^2\).

Write the product as \((2m)^2 - 3^2\), which simplifies to \(4m^2 - 9\).

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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.

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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.

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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.

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