Terms and Numerical Coefficients in Algebraic Expressions

Introduction:
In algebra, expressions are made up of terms, which consist of variables, constants, and coefficients. The coefficients are the numerical values that multiply the variables or constants in a term. Understanding the terms and coefficients in an algebraic expression is essential for simplifying and solving equations.

Terms:
A term in an algebraic expression is a combination of a coefficient and one or more variables, separated by multiplication or division. Terms can also contain constants, which are numbers without variables.

In the given expressions:
1) 3xy:
- The term "3xy" consists of two variables, x and y, which are multiplied together.
- The coefficient is 3, which is the numerical value that multiplies the variables.
- The term "3xy" contains the variables x and y, and the coefficient is 3.

2) 6z:
- The term "6z" consists of one variable, z, without any other variables.
- The coefficient is 6, which is the numerical value that multiplies the variable.
- The term "6z" contains the variable z, and the coefficient is 6.

3) 8y - 3z:
- This expression has two terms: 8y and -3z.
- The term "8y" consists of one variable, y, and the coefficient is 8.
- The term "-3z" consists of one variable, z, and the coefficient is -3.
- The negative sign (-) in front of the coefficient indicates a negative coefficient.

4) 1:
- The term "1" is a constant, which is a number without any variables.
- The coefficient is 1, which is the numerical value of the constant.

Summary:
- Terms in algebraic expressions consist of coefficients and variables, separated by multiplication or division.
- Coefficients are the numerical values that multiply the variables or constants in a term.
- The given expressions contain terms with variables x, y, and z, and the coefficients are 3, 6, 8, -3, and 1.
- Understanding the terms and coefficients in algebraic expressions is important for solving equations and simplifying expressions.