91Ó°ÊÓ

An algebraic expression is a mathematical phrase that can include numbers, variables, and operations. It represents a value, but unlike an equation, it doesn't have an equality sign. In the expression given in the exercise, we see multiple terms with variables and constants. Here, the variables are raised to different powers, known as exponents. Understanding algebraic expressions is crucial because it forms the foundation of algebra.
Examples of algebraic expressions include:

• 3x + 7y
• 5a^2 - 4b + 12
• 9t^3 - 11t + 5t + t^2

Every part of these expressions, including the numbers and the variable parts, plays a role in simplifying and solving the equation. Always remember to pay attention to the signs (positive or negative) when working with these terms!

Writing terms in descending order means arranging them from the highest power of the variable to the lowest. In the context of our problem, we start with the term containing the highest exponent of the variable 't', and end with the term of the lowest exponent.
For example, in the expression:
9t^3 + t^2 - 11t + 5t We start with the term 9t^3, then t^2, followed by -11t and finally 5t. Writing in descending order helps us clearly see the structure of the expression. It also makes combining like terms easier.
When terms are jumbled up, it's harder to identify like terms and simplify correctly.
Here's how you should proceed:

• Identify the highest exponent.
• Write that term first.
• Continue writing the next highest exponent terms until you reach the constant, if there is one.

This systematic approach ensures you don't miss any terms, and your work stays organized.

Simplifying an algebraic expression involves combining like terms to make the expression as concise as possible. Like terms are terms that have the same variable raised to the same power. In the provided expression, we have like terms -11t and 5t.
Here's a step-by-step method to simplify:

• Arrange the expression in descending order.
• Identify like terms.
• Combine the coefficients of like terms.
• Write the simplified expression.

In our example, combining -11t and 5t results in -6t. This leaves us with: 9t^3 + t^2 - 6t. Notice how this new expression is simpler and cleaner.
Simplifying expressions makes them easier to work with in algebraic operations, such as solving equations or evaluating functions.