like terms
Imagine you are tidying a shopping basket: you can stack three apples with two more apples to get five apples, but you cannot merge apples with oranges into a single pile. In algebra, an apple might be the symbol x and an orange might be the symbol y. Like terms are the algebraic “same kind” — terms whose variable parts are identical, so they can be pooled together.
More precisely, two terms are like terms when they have exactly the same variables raised to exactly the same powers. The number in front (the coefficient) does not have to match; only the variable part must agree. So 3x and -7x are like terms, and 4x^2 and x^2 are like terms, but 4x and 4x^2 are not — the powers differ. Constants with no variable at all (like 5 and -2) are also like terms with each other.
A common slip is to treat x and x^2 as the same because they share the letter x. They do not: x means x to the first power and x^2 means x times x, so their variable parts differ. Matching the letters is not enough — the exponents must match too.
In 4x + 3y - 2x + 5, the like terms are 4x and -2x (both have variable part x); 3y stands alone; 5 is a lone constant.
Like terms share an identical variable part.
Order inside a product does not matter: 3xy and 5yx are like terms, since xy and yx name the same variable part.