Unit 1: Variables and Variable Expressions

1a. Identify parts of algebraic expressions, including terms, factors, and coefficients

  • How do you refer to the different parts of an algebraic expression?

Algebraic expressions are often made up of several parts. For example, the algebraic expression \(3x^2+5x-3\) is made up of three parts, which are called terms. The terms are \(3x^2, 5x\), and \(-3\). Each term is made up of its own parts. For example, \(3x^2\) is made up of the coefficient, which is \(3\), and the variable, which is \(x^2\). The term \(-3\) has no variable part, so it is called a constant since the value of \(-3\) does not change. 

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1b. Evaluate algebraic expressions for the given values of the variables

  • How do you evaluate an algebraic expression for a specific value?

Sometimes, an algebraic expression represents a situation, and a specific value is assigned to the variable. For example, \(4x+7\) it is an algebraic expression, and you could be asked to evaluate the expression \(x=2\). Since you are being told that \(x=2\), you will replace, or substitute, the 2 in place of the \(x\). After substituting, you will find \(4(2)+7\). Following the order of operations, you can multiply 4 and 2, then add 7 to find the answer, which is 15. 

Similarly, you could have an expression with multiple variables where you need to substitute for all the variables. For example: Evaluate \(5x+2y-3z\) when \( x=1\), \(y=3\), \(z=5\). In this case, you would substitute for all three variables at the same time, then follow the order of operations to find the answer:

\(5(1)+2(3)-3(5)=5+6-15=-4\)

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1c. Apply commutative, associative, and distributive properties of real numbers to simplify algebraic expressions

  • What properties can you use to simplify algebraic expressions?

When working with algebraic expressions, it is often helpful to first simplify the expression. When simplifying expressions, these properties are helpful to know and apply:

Commutative property: Addition and multiplication can be performed in any order without changing the value. For example, \(5+3=3+5\) and \(2 \times 3 = 3 \times 2\).

Associative property: Addition and multiplication can be regrouped without changing the value. For example, \((2+3)+5=2+(3+5)\) and \((3 \times 5)7=3(5 \times 7)\).

Distributive property: Multiplication can be distributed across either addition or subtraction within parentheses. For example, \(3(x+5)=3x+3 \times 5=3x+15\).

To review, see:



Unit 1 Vocabulary

This vocabulary list includes terms you will need to know to successfully complete the final exam.

  • algebraic expression
  • associative property
  • coefficient
  • commutative property
  • constant
  • distributive property
  • evaluate
  • order of operations
  • simplify
  • substitute
  • term
  • variable
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