In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product.√6 (4√6 - 3√2)

Verified step by step guidance

1. Step 1: Distribute the \( \sqrt{6} \) to each term inside the parentheses.
2. Step 2: Multiply \( \sqrt{6} \) by \( 4\sqrt{6} \).
3. Step 3: Multiply \( \sqrt{6} \) by \( -3\sqrt{2} \).
4. Step 4: Simplify the expression \( \sqrt{6} \times \sqrt{6} \) to \( 6 \).
5. Step 5: Combine and simplify the terms, if possible, to get the final expression.

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, etc. In this context, √6 and √2 are square roots that can be manipulated according to algebraic rules. Understanding how to simplify and combine these expressions is crucial for solving problems involving radicals.

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term within a parenthesis. In the given problem, applying the distributive property is essential to multiply √6 by each term in the expression (4√6 - 3√2).

Simplifying Radical Expressions

Simplifying radical expressions involves reducing them to their simplest form, which may include combining like terms or rationalizing denominators. In this exercise, after applying the distributive property, it is important to simplify any resulting radical expressions to achieve the final answer in its simplest form.