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Chapter 1: Problem 49

Simplify each algebraic expression. $$11 a-3 a$$

Short Answer

Expert verified
The simplified form of the expression '11a - 3a' is '8a'.

Step by step solution

01

Identify Like Terms

In the expression, '11a' and '-3a' are like terms because they both contain the variable 'a' raised to the same power of '1'.
02

Combine Like Terms

The like terms can be combined by adding or subtracting them. In this case, as the expression is '11a - 3a', subtract '3a' from '11a'. This results in '8a'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Like Terms
Understanding like terms is crucial in working with algebraic expressions. **Like terms** are terms that contain the same variable raised to the same power. For example, in the expression \(11a - 3a\), both terms include the variable \(a\) raised to the power of 1, thus they are like terms.
Recognizing like terms allows us to simplify algebraic expressions by combining them efficiently.
Terms can be added or subtracted from each other only if they are like terms.
Remember:
  • Check for the same variable.
  • Ensure the variable is raised to the same exponent.
Practicing the identification of like terms will improve your ability to simplify complex expressions.
Simplifying Expressions
**Simplifying expressions** involves reducing an algebraic expression to its simplest form. This means combining like terms and performing basic mathematical operations.
In the context of our example, \(11a - 3a\), we simplify by identifying the like terms first, which are \(11a\) and \(-3a\). We then subtract \(3a\) from \(11a\) to get \(8a\).
Key steps to follow when simplifying:
  • Identify and group together like terms.
  • Perform addition or subtraction on the coefficients while keeping the variable unchanged.
Simplifying expressions is a foundational skill in algebra, making further algebraic manipulations easier.
Variables in Algebra
**Variables** are a central component in algebra. They are symbols, usually letters like \(a, b, x, y\), which represent unknown or changeable numbers.
When we refer to variables, we indicate that particular quantities could vary or are yet to be determined.
In expressions like \(11a - 3a\), \(a\) is a variable. Understanding variables is essential because:
  • They allow flexibility in representing general algebraic relationships.
  • They make it easier to express mathematical equations and formulas.
  • We can perform different operations using variables, as seen when simplifying expressions.
Grasping the concept of variables enables you to tackle a wide range of algebra problems effectively.

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