Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. (2 + √3) (2 - √3)

Verified step by step guidance

1. Recognize that the expression \((2 + \sqrt{3})(2 - \sqrt{3})\) is a difference of squares.
2. Recall the formula for the difference of squares: \((a + b)(a - b) = a^2 - b^2\).
3. Identify \(a = 2\) and \(b = \sqrt{3}\) in the expression.
4. Apply the difference of squares formula: \((2)^2 - (\sqrt{3})^2\).
5. Simplify each term: \(2^2 = 4\) and \((\sqrt{3})^2 = 3\), then subtract the results.

Key Concepts

Difference of Squares

The difference of squares is a fundamental algebraic identity that states that for any two terms a and b, the expression (a + b)(a - b) equals a² - b². This identity is useful for simplifying expressions involving binomials, particularly when one term is the square root of another.

Radicals

Radicals are expressions that involve roots, such as square roots. In this context, √3 represents the positive square root of 3. Understanding how to manipulate and simplify radical expressions is essential for performing operations involving them, especially when combined with other algebraic terms.

Simplification of Expressions

Simplification involves reducing an expression to its simplest form, making it easier to understand or compute. This process often includes combining like terms, applying algebraic identities, and reducing fractions. In the given problem, simplifying the product of the binomials will yield a clearer result.