\[ (x+a)(x+b)=(x+a) x+(x+a) b \] Associative Property of Multiplication Commutative Property of Addition Distributive Property Associative Property of Addition Commutative Property of Multiplication

To determine which property is being illustrated by the equation \[ (x+a)(x+b)=(x+a) x+(x+a) b, \] let's analyze both sides of the equation step by step. 1. **Left Side:** - The left side is \((x+a)(x+b)\). This represents the multiplication of two binomials. 2. **Right Side:** - The right side is \((x+a)x + (x+a)b\). This shows that we are distributing \((x+a)\) across the terms \(x\) and \(b\). Now, let's identify the property being used: - The left side is a product of two expressions, while the right side shows the result of distributing \((x+a)\) over the sum \(x + b\). This is a clear application of the **Distributive Property**, which states that \(a(b+c) = ab + ac\). Thus, the equation demonstrates the **Distributive Property**. The other properties mentioned (Associative Property of Multiplication, Commutative Property of Addition, Associative Property of Addition, and Commutative Property of Multiplication) do not apply to this equation as it specifically illustrates the distribution of multiplication over addition. Therefore, the correct answer is: **Distributive Property**.