Name: __________________________
Math Apps 6.1 Guided Notes
The Fundamentals of Algebra
A ____________________ usually represented by a letter, is a quantity that can change. It represents
unknown values in a situation.
An __________________________________ is a combination of variables, numbers, operation symbols,
and grouping symbols. Some examples of algebraic expressions are
ALGEBRAIC EXPRESSIONS
Algebraic expressions are made up of one or more terms. Terms are the pieces in an expression that are
separated by addition or subtraction signs. In the expression 8x2 + 6x - 3, each of 8x2, 6x, and - 3 is a
term. The expression 111 has just one term, namely 111.
Every term has a _______________________________, or just coefficient. This is the number part of a
term, like the 8 in 8x2.
Example problems
Identify the terms of the algebraic expression, and the coefficient for each term.
Use the distributive property to multiply out the parentheses.
(a) 5(3x + 7)
(b) - 3(6A - 7B + 10)
SIMPLFYING ALGEBRAIC EXPRESSIONS
When two terms have the same variables with the same exponents, we will call them
___________________________.
To add or subtract like terms (i.e., combine like terms), add or subtract the numerical coefficients of the
like terms.
Example problems
Combine like terms for each, if possible.
(a) 9x – 20x
(b) 3x2 + 8x2 – 2x2
(c) 6x + 8x2
Simplify each expression.
(a) 9x – 7y + 18 – 27 + 6y – 10x
(b) 3x3 + 4x2 – 6x + 10 – 7x2 + 4x3 + 2x – 6
Simplify the expression
8(3x2 + 5) + 3(2 – x) – (5x2 + x).
EVALUATING ALGEBRAIC EXPRESSIONS
Algebraic expressions almost always contain variables, which can be any number. But when we
substitute numbers in for the variables, the result is an arithmetic problem. Finding the value of this
problem is called __________________________the expression.
Example problems
Evaluate 9x – 3 when x = 5.
Evaluate 5x2 – 7y + 2 when x = – 3 and y = 6.
A salesperson at a popular clothing store gets a $600 monthly salary and a 10% commission on
everything she sells. The expression 0.10x + 600 describes the amount of money she earns each month,
where x represents the dollar amount of sales. If she had net sales of $13,240 in July, how much did she
earn?
The state of Florida has a sales tax of 6%.
(a) Write an expression for the total cost of an item purchased in Florida, including sales tax. The
variable should represent the cost of the item before tax.
(b) John bought an iPhone at a store in Hollywood, Florida. The price was $349. What was the total cost
John paid, including tax?
While shopping at her favorite department store, Carmen found a dress she’s been hoping to buy on the
40%-off clearance rack.
(a) Write an algebraic expression representing the new price of the dress before tax, then one for the
total price including tax. Use 6% as the sales tax rate.
(b) If the original price of the dress was $59, find the discounted price, and the total amount that Sally
would pay including tax.