Identify the property illustrated in each statement. Assume all variables represent real numbers. 6 • 12 + 6 • 15 = 6(12 + 15)

Verified step by step guidance

1. Observe the given expression: \(6 \cdot 12 + 6 \cdot 15 = 6(12 + 15)\).
2. Notice that the number 6 is multiplied by both 12 and 15 separately on the left side.
3. On the right side, 6 is factored out and multiplied by the sum of 12 and 15 inside the parentheses.
4. This illustrates the Distributive Property, which states that for any real numbers \(a\), \(b\), and \(c\): \(a \cdot b + a \cdot c = a(b + c)\).
5. Therefore, the property shown is the Distributive Property of multiplication over addition.

Key Concepts

Distributive Property

The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend separately and then adding the products. In algebraic form, a(b + c) = ab + ac. This property is fundamental for simplifying expressions and solving equations.

Multiplication over Addition

This concept highlights how multiplication interacts with addition, allowing the factor outside the parentheses to be distributed to each term inside. It ensures that operations are performed correctly and consistently, preserving equality in expressions.

Algebraic Expression Simplification

Simplifying algebraic expressions involves applying properties like distributive, associative, and commutative to rewrite expressions in simpler or more useful forms. Recognizing these properties helps in manipulating and solving equations efficiently.