Distributive property

Definition

The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products. Mathematically, it is expressed as $a(b + c) = ab + ac$.

5 Must Know Facts For Your Next Test

1. The distributive property applies to both addition and subtraction: $a(b + c) = ab + ac$ and $a(b - c) = ab - ac$.
2. It can be used to simplify algebraic expressions by eliminating parentheses.
3. The distributive property is foundational for understanding polynomial multiplication.
4. This property holds true for real numbers, integers, rational numbers, and complex numbers.
5. Using the distributive property can help solve equations by isolating variables.

Review Questions

• How would you apply the distributive property to simplify $3(x + 4)$?
• Use the distributive property to expand and simplify $2(3y - 5)$.
• Explain how the distributive property can be used to solve the equation $4(x + 2) = 20$.

Related terms

Associative Property: A property of addition and multiplication that states the way in which numbers are grouped does not change their sum or product: $(a + b) + c = a + (b + c)$ and $(ab)c = a(bc)$.

Commutative Property: A property of addition and multiplication that states changing the order of numbers does not change their sum or product: $a + b = b + a$ and $ab = ba$.

Expression: A combination of numbers, variables, and operations without an equality sign. Examples include $3x + 4$, $7 - y$, or $\frac{1}{2} x^2$.