91Ó°ÊÓ

In algebra, like terms are terms that contain the same variables raised to the same power. These terms can be easily combined, much like grouping similar items together. When looking at an algebraic expression like \(3b - 5 - 10b - 4\), it's important to first identify these like terms.
For example, the terms \(3b\) and \(-10b\) are like terms because they both have the variable \(b\). Meanwhile, the terms \(-5\) and \(-4\) are also like terms, as they are both constants (numbers without variables).
To recognize like terms, follow these tips:

• Look for terms with the exact same variable(s).
• Ensure the variables are raised to identical powers.
• Determine if there are constant terms that can be grouped.

Once you have identified like terms in an algebraic expression, the next step is to simplify the expression by combining these terms. This process helps make expressions shorter and easier to understand.
For the expression \(3b - 5 - 10b - 4\), begin by combining the like terms that contain the variable \(b\):

• Combine \(3b\) and \(-10b\) by adding their coefficients: \(3 - 10\). This results in \(-7b\).

Then, combine the constant terms:

• Combine \(-5\) and \(-4\). This results in \(-9\).

The resulting simplified expression is \(-7b - 9\).
By consistently combining like terms, you can effectively simplify algebraic expressions, leading to more manageable equations or tasks in math exercises.

Algebraic expressions are combinations of numbers, variables, and operations. They represent mathematical relationships and can contain one or more terms. Simplifying these expressions is a fundamental skill in algebra.
For example, the expression \(3b - 5 - 10b - 4\) includes variable terms, \(3b\) and \(-10b\), and constant terms, \(-5\) and \(-4\). Algebraic expressions can often appear complex at first glance, but by breaking them down into their components — like terms and constant terms — they become much easier to handle.
Here’s a quick checklist to approach algebraic expressions:

• Identify all the terms in the expression.
• Determine which terms are "like" so they can be combined.
• Simplify by performing necessary operations (addition, subtraction, etc.).

Developing the ability to simplify algebraic expressions is crucial for solving equations and understanding more advanced mathematical concepts.