Skill: 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.