Problem 49 - Introductory and Intermediate Algebra for College Students 4th

Question

Simplify each algebraic expression. $$25 y+(-12 y)$$

Step-by-Step Solution

Answer

The simplified expression is \(13y\).

Step 1: Identify Variable and Coefficients

For the algebraic expression \(25y + (-12y)\), the variable we are working with is y. The coefficients are 25 and -12.

Step 2: Simplify Algebraic Expression

Next, we need to perform the addition operation. We are basically adding the two coefficients together: \(25 + (-12) = 13\). Hence, the simplified algebraic expression is \(13y\).

Key Concepts

Coefficients

In algebraic expressions, coefficients play a key role. They are the numerical parts that appear in front of variables. For example, in the expression \(25y + (-12y)\), the numbers 25 and -12 are coefficients.

• Co-efficients indicate how many times the variable is being added together.
• They can be positive or negative.
• Understanding coefficients helps us perform operations like addition and subtraction in expressions.

When simplifying expressions, we often focus on their coefficients. This allows us to combine terms effectively. In our example, combining the coefficients, 25 and -12, gives us a new coefficient of 13.

Variables

Variables are symbols in algebraic expressions that stand for numbers. They are like placeholders, representing unknown values. In the expression \(25y + (-12y)\), the variable is \(y\). This letter can represent any number.

• Variables allow for the generalization of mathematical relationships.
• They help in forming equations that can be solved to find specific values.

Using variables, we can build and manipulate expressions to solve problems. Understanding variables is crucial because they provide a way to express mathematical ideas flexibly.

Simplification of Expressions

Simplification is the process of making an expression easier to understand or solve. When we simplify, we try to reduce expressions to their simplest form. For \(25y + (-12y)\), simplification involves combining like terms.

• Like terms have the same variable raised to the same power.
• We add or subtract their coefficients to simplify.

In our example, \(25y + (-12y)\), we just add the coefficients: \[\begin{align*}&25 + (-12) = 13\end{align*}\]Thus, the simplified expression is \(13y\). Simplification makes algebraic expressions easier to work with in further calculations.