What is Like Terms

Math 6

1. Fundamental Concepts

Definition: Like terms are terms whose variable parts (including variables and their exponents) are completely identical. Coefficients do not affect whether terms are like terms.

2. Key Concepts

Judgment Criteria: Two terms are like terms if they contain the same variables with identical exponents for each corresponding variable. Coefficients can differ.
Constant Terms: All constant terms (e.g., 10, -4, 2.5) are like terms.

3. Examples

(1) Easy Difficulty

Question: Identify like terms from 3x, 5x, 2z, 8z.
Analysis: 3x and 5x are like terms (both have variable x with exponent 1); 2z and 8z are like terms (both have variable z with exponent 1).

(2) Medium Difficulty

Question: Identify like terms from 2x², 7x², 3x, 5y.
Analysis: 2x² and 7x² are like terms (both have variable x with exponent 2); 3x (x with exponent 1) and 5y (variable y) are not like terms.

(3) Hard Difficulty

Question: Identify like terms from 4xy², -2xy², 3x²y, 5y²x.
Analysis: 4xy², -2xy², and 5y²x are like terms (variables x and y with exponents 1 and 2, respectively; order of variables does not matter). 3x²y (x with exponent 2, y with exponent 1) is not a like term with the others.

4. Problem-Solving Techniques

Step-by-Step Approach:
1. Ignore coefficients and identify the variables and their exponents in each term.
2. Group terms with identical variable parts.
3. Verify that each group has the same variables and exponents; constant terms form a separate group.
Strategies: Use the reverse distributive property (e.g., \(ax + bx = x(a + b)\)) to simplify like terms. Analogies (e.g., categorizing "apples" and "pears") can aid understanding.