Understanding Algebraic Expressions

Algebraic expressions are combinations of numbers, variables (like \( x \) or \( y \)), and operations (such as addition, subtraction, multiplication, and division). These expressions form the building blocks of algebra.

Simplifying Expressions

To simplify an expression, combine like terms and use the distributive property. Like terms have the same variable raised to the same power.

• Distributive Property: \( a(b + c) = ab + ac \)
• Combining Like Terms: \( 3x + 5x = 8x \)

Operations with Expressions

You can add, subtract, multiply, and divide expressions just like regular numbers, but always pay attention to the variables.

• Addition/Subtraction: Only combine like terms.
• Multiplication: Use the distributive property.
• Division: Divide coefficients and subtract exponents for like bases.

Why It Matters

Mastering these basics helps you solve equations and model real-world problems, such as calculating areas, budgeting, or analyzing patterns.