Multiply. See Example 7. (√2 - √3) (√2 + √3)

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Recognize that the expression \((\sqrt{2} - \sqrt{3})(\sqrt{2} + \sqrt{3})\) is in the form of a product of conjugates, which follows the pattern \((a - b)(a + b) = a^2 - b^2\).

Identify \(a = \sqrt{2}\) and \(b = \sqrt{3}\) from the given expression.

Apply the difference of squares formula: \(a^2 - b^2 = (\sqrt{2})^2 - (\sqrt{3})^2\).

Calculate each square separately: \((\sqrt{2})^2 = 2\) and \((\sqrt{3})^2 = 3\).

Subtract the results to get the simplified expression: \(2 - 3\).

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Difference of Squares

The difference of squares is a special product formula: (a - b)(a + b) = a² - b². It simplifies multiplication by converting the product of conjugates into the difference between the squares of the two terms.

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