Terms in expressions and equations

Understanding Terms in Expressions and Equations

Introduction

• Terms are the different parts that are combined with operations (like addition, subtraction, multiplication, and division) in an algebraic expression or equation.
• Terms can be standalone numbers, letters representing numbers (variables), or combinations thereof.

Identifying Terms

• Terms are usually separated by “+” or “-“ signs. For instance, in the expression 3x + 2y - 7, the terms are 3x, 2y, and 7.
• A term can also be a coefficient (numerical factor) times a variable. For example, in 4a, 4 is the coefficient and a is the variable.

Types of Terms

• Constant Terms: These are terms that do not change. They do not contain a variable. Examples include numbers like 5, -3, 0.5, etc.
• Variable Terms: These are terms that contain one or more variables like x, y, or z. Examples include x, 3y, -z, 4xy, etc.
• Coefficient: This is the number part of a variable term that shows how many times the variable is taken. For instance, in 5x, 5 is the coefficient.

Combining Like Terms

• Like terms are terms that contain the same variables raised to the same power. For example, 4x and -3x are like terms.
• In order to be able to simplify an expression or an equation, it is important to know how to combine like terms. This involves adding or subtracting the coefficients while keeping the variable part the same.
• For example, in the expression 4x + 3 - 2x + 5, the like terms can be combined to simplify the expression to 2x + 8.

Conclusion

• Recognising and understanding terms in expressions and equations is fundamental to dealing with algebra.
• It is crucial to practice identifying, distinguishing between, and combining like terms in a variety of scenarios.
• In all instances, make sure to handle the signs (+, -) properly.