Problem 50 - Introductory and Intermediate Algebra for College Students 4th

Question

Simplify each algebraic expression. $$26 y+(-14 y)$$

Step-by-Step Solution

Answer

The simplified form of the expression '26y + (-14y)' is \(12y\).

Step 1: Identification of Like Terms

Identify '26y' and '-14y' as like terms since both contain the same variable 'y'.

Step 2: Addition of Like terms

Based on the rules of addition in algebra, we can combine these terms by performing the addition 26 - 14.

Step 3: Submission of Result

The result is \(12y\), which is the simplified form of the given expression.

Key Concepts

Like Terms in Algebra

Understanding like terms in algebra is crucial for simplifying algebraic expressions. Like terms are terms that have exactly the same variable parts, which means they have the same variables raised to the same powers. For example, terms such as '3x' and '5x' are considered like terms because they both have the variable 'x'. However, '3x' and '3y' are not like terms because they have different variables.

A common pitfall for students is mixing up terms with similar numbers but different variable components, such as '2x^2' and '2x'. Even though they both have the number 2, they are not like terms because one has 'x' squared while the other only has 'x'.

Once you've identified like terms, you can perform operations like addition and subtraction on them, which are fundamental steps in simplifying algebraic expressions. It's the similarity in variable parts that make these operations possible.

Addition of Like Terms

When it comes to the addition of like terms, it can be helpful to think of like terms as similar objects. Imagine you have 5 apples and someone gives you 3 more apples; you end up with 8 apples. Similarly, in algebra, if you have '5x' and add '3x' to it, since both terms have the variable 'x', you simply add their coefficients (the numerical part) together to get '8x'.

Here's how you do it step by step:

• Identify the like terms in the expression. Look for terms with the same variable and exponent.
• Add the coefficients of these terms together while leaving the variable part unchanged.
• Write down the simplified expression with the new coefficient and the unchanged variable part.

Remember that you can only add the coefficients when the variables are exactly the same. Trying to add or subtract terms with different variables or exponents will not result in a simplified expression.

Algebraic Expressions Simplification Steps

Simplifying algebraic expressions involves several steps to combine like terms and perform operations to reduce the expression to its simplest form. Let's break down the simplification process:

Identifying Like Terms

Start by scanning the expression for like terms. Group these terms together as it makes the simplification process more organized.

Combining Like Terms

Once grouped, add or subtract the coefficients of these like terms as applicable. Be careful with subtraction; remember to subtract the second coefficient from the first.

Applying the Order of Operations

After dealing with like terms, don't forget to follow the order of operations (PEMDAS/BODMAS) for any remaining parts of the expression. This is where you address any brackets, exponents, multiplication, and division.

Checking Your Work

Finally, always double-check your result. It's easy to make small mistakes with signs or coefficient calculations.

By following these simplification steps diligently, you will be able to consistently simplify algebraic expressions correctly, building a strong foundation in algebra that will be beneficial for advanced topics.