RWM102: Algebra

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.

To review, see Identifying Variable Parts and Coefficients of Terms.

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 is given to represent a situation, and a specific value is assigned to the variable. For example, $4x+7$ is an algebraic expression, and you could be asked to evaluate the expression at $x=2$. 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 $4(2)+7$. By 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:

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

To review, see Practice Evaluating Expressions in One Variable and Practice Evaluating Expressions in Two Variables.

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, the following 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 $(3 \times 5) \times 7 = 3 \times (5 \times 7)$.

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

To review, see:

• Commutative Laws of Addition and Multiplication
• Associative Laws of Addition and Multiplication
• Distributive Property of Multiplication Over Addition

Unit 1 Vocabulary

This vocabulary list includes terms listed above that students need to know to successfully complete the final exam for the course.

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