Distributive Property Worksheets

What is the distributive property?

The distributive property says that multiplying a sum by a number is the same as multiplying each term of the sum and then adding: $a(b + c) = ab + ac$. It is how an expression with parentheses, like $3(2x + 7)$, is rewritten without them.

The number in front multiplies every term inside the parentheses, and its sign comes along. After distributing, combine any like terms.

• Easy — $a(x + b)$ or $a(x - b)$.
• Medium — $a(bx + c)$ or $a(bx - c)$, where the $x$-term also has a coefficient.
• Hard — $ax + b(cx + d)$ or $ax - b(cx + d)$: distribute, then combine the $x$-terms.

Worked examples

Easy: $4(x - 5)$

Medium: $3(2x + 7)$

Hard: $5x - 2(3x + 4)$

The multiplier is $-2$, so both terms inside change sign:

Check your answers

Substitute a number. With $x = 1$ in the hard example: $5 - 2(7) = -9$ and $-1 - 8 = -9$.

Common mistakes

• Multiplying only the first term. $4(x - 5)$ is not $4x - 5$.
• Dropping the negative. $-2(3x + 4) = -6x - 8$, not $-6x + 8$.
• Forgetting to combine like terms. $5x - 6x - 8$ should be finished as $-x - 8$.
• Multiplying coefficients into the wrong place. $3 \cdot 2x = 6x$, not $32x$ or $6x^{2}$.

Sample problems

These problems come from the same generator as the worksheet above, three at each difficulty level. Press Generate for a fresh set.

Easy

1. $5(x + 9) =$
2. $7(x + 3) =$
3. $5(x - 5) =$

Medium

4. $3(3x - 3) =$
5. $3(4x - 7) =$
6. $5(4x + 6) =$

Hard

7. $5x + 3(2x + 7) =$
8. $6x - 4(4x + 2) =$
9. $3x + 2(4x + 5) =$

Tips for teachers and parents

• Drawing an arrow from the outside number to each term inside the parentheses is a simple habit that prevents the most common mistake.
• For Hard problems, have students write the subtraction as $+ (-2)(3x + 4)$ until the sign rule is automatic.
• The same idea, applied twice, becomes multiplying binomials in Algebra 2.

Related topics

• Simplifying Expressions Algebra
• Solving Equations Algebra
• Polynomial Multiplication Algebra 2