Problem 84 - Introductory Algebra for College Students

Question

State a form of the distributive property and give an example.

Step-by-Step Solution

Answer

The distributive property in mathematics is typically formulated as follows: 'a * (b + c) = a * b + a * c' for any numbers a, b, and c. The example we provided to illustrate this rule was 2*(3+4) = 2*3 + 2*4, which simplified to verify that both sides of the equation were equal (14 = 14).

Step 1: Presenting the Distributive Property

The distributive property in mathematics is a basic property that denotes how multiplication over a sum or subtraction operates. It is typically formulated as follows: For any numbers a, b, and c\(a * (b + c) = a * b + a * c\)or\(a * (b - c) = a * b - a * c\)

Step 2: Providing an Example

Let's provide a straight-forward example using simple integers. Let a = 2, b = 3, and c = 4.Apply the distributive property:\(2 * (3 + 4) = 2 * 3 + 2 * 4\)Hence, \(2 * 7 = 6 + 8\)Simplify both sides of the equation:14 = 14As seen, both sides are equal, thus accurately exemplifying the distributive property.