Properties of Mathematics: The Distributive Property

How can we evaluate the expression (3-2c)(3+2c) using properties in Mathematics?

Let's explore the step-by-step process of evaluating this mathematical expression.

Evaluating (3-2c)(3+2c)

Using the Distributive Property in Mathematics, we evaluate the expression (3-2c)(3+2c) to be 9 - 4c^2.

The equation asked to evaluate is a product of two binomials. In Mathematics, when handling operations such as these, the Distributive Property is usually applied. This property states that the multiplication of a number (or expression) by a sum (or difference) equals the sum (or difference) of the products.

Here we can rewrite the expression (3-2c)(3+2c) using the form a(b+c), in which case a=3, b=-2c, and c=2c. By the Distributive Property, we can multiply each term in the first expression by every term in the second expression, which gives: 3*3 + 3*2c - 2c*3 - 2c*2c. We then simplify to get 9 + 6c - 6c - 4c^2.

The term 6c - 6c cancels out and we are left with the evaluated expression: 9 - 4c^2. This process showcases the importance and power of utilizing mathematical properties like the Distributive Property to simplify complex expressions and equations.