Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms (both have x to the first power), but 3x and 3x² are not. Combining like terms means adding or subtracting their coefficients: 3x + 5x = 8x, and 7y² − 2y² = 5y². This is the algebraic version of the idea that you can only add things of the same kind — you can add 3 apples and 5 apples to get 8 apples, but you cannot combine 3 apples and 5 oranges. Simplifying expressions by combining like terms is a fundamental skill used in every subsequent algebra topic.
Use algebra tiles or color-coded cards to make the concept concrete — same shape/color means "like." Sort terms into groups before combining. Practice with expressions that have multiple variable types (e.g., 3x + 2y + 5x − y = 8x + y). Emphasize that constants are like terms with each other.
You already know how to add and subtract integers, and you know that a variable expression like 3x means "3 times x" — the coefficient counts how many copies of the variable you have. Combining like terms builds directly on this: it is just adding and subtracting counts of the same thing.
Think of it in terms of fruit, an analogy that makes the logic transparent. Three apples plus five apples equals eight apples — you add the counts because the units match. But three apples plus five oranges cannot be simplified to a single number; you must keep them separate as "3 apples + 5 oranges." Variable terms work identically: 3x + 5x = 8x because both measure copies of x. But 3x + 5y cannot be simplified — x and y are different "units," and merging them would be like adding apples and oranges.
The underlying mechanism is the distributive property (from your properties-of-operations work): 3x + 5x = (3 + 5)x = 8x. You are factoring out the variable and adding the coefficients. This is why you add the coefficients and leave the variable unchanged — the variable is the common unit, and the coefficients are the counts being summed. Subtraction works the same way: 7y² − 2y² = (7 − 2)y² = 5y².
With multiple variable types, the strategy is to sort before you simplify. Given 4x + 2y + 3x − y, group by type: (4x + 3x) + (2y − y) = 7x + y. Work one group at a time. And remember: powers are part of the term's identity. The terms 3x² and 5x are not like terms. x² is "copies of x-squared" and x is "copies of x" — they measure completely different quantities, just like square feet and feet are different units. You cannot combine them, and you must never add the exponents (3x + 5x ≠ 8x², because you are counting copies, not multiplying).