Algebraic Expressions and Operations

Key Ideas of Algebraic Expressions

Pronumeral (Variable): A symbol (commonly a letter) used to represent an unknown number.
Algebraic Expression: Composed of one or more terms connected by addition or subtraction. They can involve:
- Terms: Groups formed by numbers and pronumerals (variables).
- Coefficient: A number that multiplies a pronumeral in a term. For example, in 3y, 3 is the coefficient of y.
- Constant Term: A term without any pronumerals; only a number, such as 7 or -3.
- Combination of terms can involve addition, subtraction, multiplication, and division.

Single Term: May consist of:
- Just a constant (e.g., 5)
- A pronumeral (e.g., x)
- A combination of both (e.g., 3xy)
Multiple Terms: Connected by addition or subtraction (e.g., 2x + 3y - 4).
Classifying Terms:
- Example: For 4xy + 5y + 8
- Number of Terms: 3
- Constant Term: 8
- Coefficient of y: 5

Adding/Subtracting: Combine like terms.
- Example: From cy + 3y where c = 2 and y = 3, simplified gives 6 + 9
Multiplication: Apply the distributive property.
- Example: For 3x(2y), results in 6xy.
Substitution: Replace pronumerals with numbers to evaluate expressions.
- Example: If a = -6, then:
- For a + 9: -6 + 9 = 3
- For 12 - a: 12 - (-6) = 18
- For (a + 6)²: (-6 + 6)² = 0

Practice Questions: Evaluate and determine components of given expressions:
1. For x=2, y=3 evaluate the expressions:
- cy + 3y
- 2 - 8/2
1. Identify the number of terms, constant term, and coefficients in various expressions.
Key Examples:
- Simplifying 2x² - 4 + 4 results in 2x² where:
- Number of Terms: 1
- Constant Term: 0
- Coefficient of x²: 2

Always identify coefficients, constant terms, and the number of terms in algebraic expressions for evaluating or simplifying them.
Use substitution for simplifying expressions and ensuring to apply proper mathematical operations accordingly.
Understanding the structure and vocabulary of algebra is essential for solving problems effectively.