Combine like terms and use the distributive property to rewrite expressions. | Equivalent expressions | SAT Math

When you see parentheses and multiple terms, distribute any multipliers first, then group and combine terms with the same variable and exponent.

Core Idea

Distribute multipliers across parentheses first, then add or subtract coefficients of terms that share the same variable and exponent. Order matters—distribute before you combine.

Understanding

The distributive property says $𝑎 (𝑏 + 𝑐) = 𝑎 𝑏 + 𝑎 𝑐$ . When a negative sign or fraction sits outside parentheses, it multiplies every term inside—not just the first one. Missing the last term is the single most common error on these questions.

After distributing, scan for like terms: same variable, same exponent. Only the coefficients change when you combine like terms. Constants (bare numbers with no variable) are like terms with each other.

When an expression has nested operations—a fraction times a group minus another group—work left to right. Distribute the fraction first, then distribute the subtraction, then combine.

Step by Step

Distribute any coefficients, fractions, or negatives across each set of parentheses.
Identify like terms (same variable and same exponent).
Combine like terms by adding or subtracting their coefficients.
Write the simplified result in standard form (highest degree first).

Misconceptions

Distributing only to the first term inside parentheses— $3 (2 𝑥 + 5)$ becomes $6 𝑥 + 5$ instead of $6 𝑥 + 15$ .
Forgetting that a minus sign in front of parentheses flips the sign of every term inside, not just the first.
Combining terms that aren't actually alike—adding $3 𝑥 2$ and $2 𝑥$ to get $5 𝑥 2$ or $5 𝑥 3$ .

Question

Worked Example

Which of the following expressions is equivalent to $13 (9 𝑥 - 6) - 2 (𝑥 + 5)$ ?

Select an answer to see the explanation