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An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like a, x, or y), and operations (such as add, subtract, multiply, and divide). In our exercise, (9+2)a is an algebraic expression with one variable, a. The beauty of algebraic expressions lies in their ability to represent numbers in a general form, making it possible to perform a wide range of calculations and solve problems.

When we look at (9+2)a, we understand that it represents the sum of 9 times a and 2 times a, even before doing any specific calculations. Being familiar with algebraic expressions is essential, as they are the foundation of algebra and appear in virtually every area of math beyond arithmetic.

To simplify an algebraic expression means to make it as ‘simple’ as possible. This could involve combining like terms, which are terms with the same variables raised to the same power, or using properties of operations to make the expression easier to understand or use.

In our given exercise, we simplify the expression (9+2)a to 11a. This is a more straightforward expression because it conveys the equivalent mathematical concept in fewer terms which makes it quicker and easier to work with in equations and further mathematical operations.

Combining Like Terms

As an example of simplifying, in our problem, we combine 9a and 2a into 11a because they are like terms, and combining them gives us a tidier and more efficient version of the expression.

Properties of operations are rules that apply to numbers and operations, allowing us to transform and manipulate expressions in a consistent and logical manner. One such property is the Distributive Property, which we've used in our exercise.

The Distributive Property states that multiplying a sum by a number is the same as doing each multiplication separately. Mathematically, it means that a(b + c) = ab + ac.

This property is very useful in simplifying algebraic expressions and solving equations. For instance, instead of multiplying (9+2) by a to get 11a, we could distribute a into 9 and 2 separately, getting 9a + 2a, which then simplifies to 11a. Understanding and applying these properties is crucial for anyone who wants to master algebra and other advanced mathematical subjects.