Skill: Identify like terms

To identify like terms, compare their variable parts.

• The variables must be the same.
• Their exponents must also be the same.
• The numerical coefficients may be different.
• Constants, which have no variables, are like terms with other constants.

For example, consider:

$$6a^2+3ab-4a^2+9-2a+5ab-1$$

Step 1: Look at each term’s variable part.

• $6a^2$ has variable part $a^2$.
• $3ab$ has variable part $ab$.
• $-4a^2$ has variable part $a^2$.
• $9$ is a constant.
• $-2a$ has variable part $a$.
• $5ab$ has variable part $ab$.
• $-1$ is a constant.

Step 2: Group terms with identical variable parts.

• $6a^2$ and $-4a^2$ are like terms.
• $3ab$ and $5ab$ are like terms.
• $9$ and $-1$ are like terms.
• $-2a$ has no other matching term, so it has no like term in this expression.

The coefficients can be different, but the variable part must match exactly. For example, $a^2$ and $a$ are not the same, so $6a^2$ and $-2a$ are not like terms.