Combining Like Terms

Like terms have exactly the same variable part. 5x and 3x are like terms, so 5x + 3x = 8x. You are counting x's.

These are not like terms: 5x and 5x² (different exponents), or 5x and 5y (different letters). They stay separate.

When you combine, only the coefficients change. 5x + 3x is 8x, never 8x².

Keep each term's sign attached as you rearrange. In 7x − 4y − 2x, the terms are 7x, −4y and −2x, giving 5x − 4y.

Combining like terms is the distributive property applied in reverse:

5x + 3x = (5 + 3)x = 8x

The variable part must match exactly — same variables raised to the same powers — because that shared factor is what gets pulled out. x and x² share no common variable factor that leaves numbers behind, so no such factoring exists.

This is the same principle as adding fractions with a common denominator and as adding decimals aligned by place value: you may only add coefficients attached to identical units. Algebra simply lets the unit be x² or xy rather than "hundredths."

Note that terms may be reordered freely because addition is commutative and associative — but subtraction is neither, which is why converting every subtraction to "plus a negative" before rearranging is the safer habit.