Table of Contents

1. Algebraic Expressions
   1. Definition
   2. Components of an Expression
   3. Examples of Expressions
2. Simple Operations in R
   1. Addition Example
   2. Subtraction Example
   3. Polynomial Example
3. Conclusion

Algebraic expressions are combinations of variables, constants, and operations. In this section, we will explore how these expressions are formed and manipulated.

Algebraic Expressions

Definition

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add, subtract, multiply, and divide).

Components of an Expression

• Variables: Symbols that represent numbers. E.g., x, y, z.
• Constants: Fixed values. E.g., 3, -5, 2/3.
• Operators: Symbols that represent operations. E.g., + (addition), - (subtraction), * (multiplication), / (division).

Examples of Expressions

• \( 3x + 4 \)
• \( 5y - 7 \)
• \( 2x^2 + 3x - 5 \)

Simple Operations in R

We will use R to perform some basic operations on algebraic expressions.

Addition Example

x <- 2 # Assign a value to x
expression <- 3 * x + 4
print(expression)

Subtraction Example

y <- 5 # Assign a value to y
expression <- 5 * y - 7
print(expression)

Polynomial Example

Polynomials will be explained in further chapters, but it's also an expression.

x <- 1 # Assign a value to x
expression <- 2 * x^2 + 3 * x - 5
print(expression)

Conclusion

Understanding algebraic expressions is fundamental in algebra. They form the basis for more complex topics like equations, functions, and beyond.