Identify like terms

Like terms have identical variable parts—the same variables raised to the same whole-number exponents—while their numerical coefficients may differ; constants form a like-term group. The learner distinguishes, for example, $3x$ and $-5x$ from $3x^2$ and $3y$ , and understands that only like terms can be combined through addition or subtraction, supporting the simplification of algebraic expressions. The focus is on numerical coefficients and familiar variables, not advanced polynomial generalizations.

Detailed Explanation: Identify like terms

Like terms have exactly the same variable part. This means they contain:

the same variables,
raised to the same exponents.

Their numerical coefficients can be different. Constants, which have no variables, are also like terms with one another.

Consider the expression

4x+3y-2x+7+x^2-4.

Step 1: Look at each term

The terms are

4x,\quad 3y,\quad -2x,\quad 7,\quad x^2,\quad -4.

Step 2: Group terms with identical variable parts

$(4x)$ and $(-2x)$ are like terms because both have the variable part $x$ .
$7$ and $(-4)$ are like terms because both are constants.
$(3y)$ has variable part $y$ , so it does not match any other term.
$(x^2)$ has variable part $(x^2)$ , so it does not match $x$ .

We can show the groups as

\left(4x-2x\right)+3y+x^2+\left(7-4\right).

Only terms in the same group can be combined. Thus, the simplified expression is

2x+3y+x^2+3.

Remember: $x$ and $(x^2)$ are not like terms, and $x$ and $y$ are not like terms.

Learn by doing: Identify like terms

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Algebraic Functions - Multiply Bracketed Terms, Same Variable

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