Problem 136 - College Algebra

Question

What is an algebraic expression? Give an example with your explanation.

Step-by-Step Solution

Answer

An algebraic expression is a mathematical phrase that combines variables, constants, and operations to represent a particular relation. For instance, the expression \(3x+4y-5\) is an algebraic expression combining variables \(x\) and \(y\), constants \(3, 4,\) and \(-5\), and the operations of addition and multiplication.

Step 1: Definition of an Algebraic Expression

An algebraic expression is a mathematical statement that consists of variables, numbers, and operations (such as addition, subtraction, multiplication, and division). Expressions are used to represent problems in mathematical terms and have no equal (=) sign.

Step 2: Components of an Algebraic Expression

There are three main components in an algebraic expression. Variables (such as x, y, z) that represent unknown values, Constants (like 1, 2, 3, etc.) which are fixed values that do not change, and Operations which are mathematical procedures like addition (+), subtraction (-), multiplication (*) and division (/), and can also include powers.

Step 3: Example of an Algebraic Expression

Here is an example of an algebraic expression: \[3x+4y-5\]. In this expression, x and y are the variables, 3, 4, and -5 are constants, and the operations are addition and multiplication.