Simplify each expression. See Example 8.10x (3)(y)

Verified step by step guidance

1. Identify the expression to simplify: \(10x \cdot 3 \cdot y\).
2. Recognize that multiplication is associative and commutative, meaning you can rearrange and group the terms as needed.
3. Group the constants together: \((10 \cdot 3)\) and the variables \(x\) and \(y\).
4. Multiply the constants: \(10 \cdot 3\).
5. Combine the result with the variables to form the simplified expression: \((10 \cdot 3)xy\).

Key Concepts

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operators. In the context of simplification, it involves combining like terms and applying the distributive property to make the expression more concise. Understanding how to manipulate these expressions is crucial for simplifying them effectively.

Distributive Property

The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term within a parenthesis. This property is essential for simplifying expressions that involve multiplication and addition, as it helps in breaking down complex expressions into simpler components.

Factoring

Factoring involves expressing an algebraic expression as a product of its factors. This concept is important in simplification because it can reveal common factors that can be canceled out, leading to a more simplified form of the expression. Recognizing factors is key to efficient simplification.