What Are Algebraic Expressions?

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

• Examples of expressions: \( 3x + 4 \), \( 2a - b \), \( 5y^2 \)
• Operations: These include adding, subtracting, multiplying, and dividing both numbers and variables.

Simplifying Expressions

To simplify an expression, combine like terms and use the distributive property to make things easier to work with.

Like terms are terms with the same variable to the same power. For example, \( 2x \) and \( 5x \) are like terms, but \( 2x \) and \( 2y \) are not.

Distributive Property

The distributive property helps you multiply a single term by everything inside a set of parentheses:

\[ a(b + c) = ab + ac \]

This property is super useful when expanding or simplifying expressions.

Why Is This Important?

Understanding expressions and operations is the first step to solving equations, modeling scenarios, and making sense of patterns in math and the real world.

Real-World Connections

• Calculating the cost of multiple items if each has the same price (like buying three shirts at $15 each: \( 3 \times 15 \)).
• Figuring out how many minutes you spend on different activities by adding times together.