Rewrite each expression using the distributive property and simplify, if possible. 15x-10x

Verified step by step guidance

1. Identify the common factor in the expression \(15x - 10x\).
2. Notice that both terms have a common factor of \(5x\).
3. Rewrite each term as a product of the common factor: \(15x = 5x \cdot 3\) and \(10x = 5x \cdot 2\).
4. Apply the distributive property: \(5x(3 - 2)\).
5. Simplify the expression inside the parentheses: \(3 - 2\).

Key Concepts

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, facilitating the simplification of expressions. In the context of the given expression, it can be applied to factor out common terms.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This process simplifies expressions by consolidating similar components, making it easier to work with algebraic expressions. In the expression 15x - 10x, this concept is crucial for arriving at the final simplified form.

Simplification of Expressions

Simplification of expressions refers to the process of reducing an expression to its simplest form. This often involves using the distributive property, combining like terms, and eliminating any unnecessary components. The goal is to make the expression easier to understand and work with, as seen in the simplification of 15x - 10x.