Problem 86 - Introductory and Intermediate Algebra for College Students 4th

Question

What does it mean to simplify an algebraic expression?

Step-by-Step Solution

Answer

Simplifying an algebraic expression means to reduce it to its simplest form by eliminating parentheses through distribution, combining like terms, and reducing fractions, so as to make the expression simpler and easy to handle.

Step 1: Define the Term

Simplifying an algebraic expression refers to the operation of reducing it to its simplest form. The aim is to make the expression as straightforward as possible without changing its value.

Step 2: Elaborate on Operations

Operations used in simplifying include removing parentheses by distributing, combining like terms, and reducing fractions when necessary. These operations ensure the expression becomes simpler to handle and understand, possibly making further algebraic manipulations easier.

Step 3: Provide Examples

For instance, the expression \(3x + 5 + 2x\) can be simplified to \(5x + 5\) by combining like terms. Another example would be, \(4(2x + 6)\), which simplifies to \(8x + 24\) by distributing the \(4\) through the parentheses.