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In algebra, like terms are terms that share the same variable raised to the same power. This means they have identical variable parts. For instance, in the expression \(14b - 5b\), both terms are considered like terms because they both have the variable \(b\). Even though the coefficients, which are the numbers in front of the variables, are different, the variable components make them like terms. The significance of identifying like terms lies in simplifying algebraic expressions efficiently. Recognizing like terms allows us to accurately add or subtract them to form a simpler expression. This simplification process is crucial in solving equations and makes managing complex expressions manageable.

Combining like terms involves performing basic arithmetic operations such as addition or subtraction to bring terms with the same variables together. This step simplifies the expression, making it easier to work with. For the expression \(14b - 5b\), you observe that both terms have the variable \(b\). Since they are like terms, you can combine them by subtracting the coefficients: \(14 - 5\). This simplification results in the term \(9b\).

Here are some additional tips for combining like terms:

• Ensure the terms have exactly the same variable parts before combining.
• Combine the coefficients by performing the appropriate arithmetic operation.
• If there are no like terms left, double-check your work to confirm accuracy.

Combining like terms is a foundational skill necessary for solving more advanced algebraic problems.

Subtraction in algebra, like with numbers, involves taking one quantity away from another. However, in algebra, it often deals with terms containing variables. For example, in our expression \(14b - 5b\), subtraction is utilized to combine like terms. You subtract the coefficient of the second term from the first: \(14 - 5\), which simplifies to \(9b\). Here, subtraction not only reduces the number of terms but simplifies the expression as well.

Key points to remember when performing subtraction in algebra:

• Check that you are subtracting the coefficients and not the variables themselves.
• Align like terms directly above or below each other if you're working vertically.
• Pay attention to negative signs, as they can change the meaning of your subtraction.

Mastery of subtraction in algebra is essential for solving equations and further manipulations in algebraic processes.