Problem 64 - Elementary and Intermediate Algebra

Question

List the terms in each expression. $$ 9+17 a+a b c $$

Step-by-Step Solution

Answer

9, 17a, abc

Step 1: Identify individual terms

Recognize that terms in an expression are separated by addition or subtraction signs. Here, we have `9 + 17a + abc`.

Step 2: List each term

List each term separately from the expression `9 + 17a + abc`. These terms are: `9`, `17a`, and `abc`.

Key Concepts

Terms in Expressions

In algebra, an expression is a combination of numbers, variables, and operations (like addition or subtraction). Each part of the expression that is separated by a plus (+) or minus (−) sign is called a term. In the example expression 9 + 17a + abc, there are three distinct terms:

• 9
• 17a
• abc

By identifying terms, we can better understand and manipulate expressions and equations.

Addition in Algebra

Addition in algebra works much like addition in arithmetic, but it includes variables. When adding terms, you combine like terms. Like terms are terms that have the same variables raised to the same power. For example, if you have an expression like 3x + 5x, you can combine these into 8x because both terms have the variable x. However, in our given expression 9 + 17a + abc, none of the terms are 'like,' so we cannot combine them further. They stay as they are: 9, 17a, abc.
Addition in algebra helps simplify complex expressions and solve equations more efficiently.

Variable Identification

A variable in algebra is a symbol, usually a letter, that represents one or more numbers. Variables can change, which means they can take on different values. In our expression 9 + 17a + abc, the variables are 'a,' 'b,' and 'c.'

• In 17a, 'a' is the variable, and 17 is the coefficient (the number multiplying the variable).
• In 'abc,' the variables are 'a,' 'b,' and 'c,' and they are all multiplied together.

Identifying variables is fundamental for understanding how to manipulate and solve algebraic expressions. It allows us to recognize the flexible parts of an equation and explore various solutions.