Distributive property

Definition

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

5 Must Know Facts For Your Next Test

1. The distributive property can be used to simplify algebraic expressions.
2. It applies to both addition and subtraction, e.g., $a(b - c) = ab - ac$.
3. This property is essential for solving equations and factoring polynomials.
4. It is also applicable in reverse; $ab + ac = a(b + c)$ can be factored out using the distributive property.
5. Understanding this property helps in performing operations with real numbers efficiently.

Review Questions

• Use the distributive property to simplify: $3(x + 4)$.
• How would you apply the distributive property to the expression $2(3y - 5) + 4$?
• Rewrite $5a + 10b$ using the distributive property in reverse.

Related terms

Associative Property:

A property of addition and multiplication that states $(a + b) + c = a + (b + c)$ and $(a \cdot b) \cdot c = a \cdot (b \cdot c)$.

Commutative Property:

A fundamental property of addition and multiplication which states that $a+b = b+a$ and $ab = ba$.

Factorization:

The process of breaking down an expression into a product of simpler expressions, often using properties like the distributive property.