1.2.1 – Algebraic Expressions, PEMDAS

• You are familiar with equations…right?

• Algebraic expressions are similar, but no equal signs (not solving for anything)– Combination of variables (letter to represent one

or more numbers) and operations (+, -, etc.)

PEMDAS

• We will encounter numerous types of algebraic expressions; some may be used to model real life scenarios or situations– 2x + 9 – 3(p – 7) + 10

• Before evaluating them, always must consider the order of operations– Gives us a guide on how to evaluate expressions correctly

• PEMDAS

• P = parenthesis– Always start on inner most set; work your way out

• E = exponents– Always check signs

• M = multiplication• D = division• A = addition• S = subtraction

• Typically, after you substitute a value for a variable, most follow the order of operations to obtain the correct answer

• Example. Evaluate 3(x + 1) – 2 if x = 4– What do you do with the x = 4 part?

• Example. Evaluate ((x + 2)/2) + 9 x 2 for x = 5

• Example. Evaluate -2 ∕2 + 6 x 4

• Example. Evaluate 4 – 3(7 + 2)

Powers

• With large scale multiplication, need a quick way to complete it– Multiplication is essentially fast hand addition

• We use powers for repeated multiplication– Two parts;– Base = factor being multiplied– Exponent = numbers of times multiplied– Example. 7 x 7 x 7 = 73

• With powers, always have to be careful about negative signs and parenthesis (use our knowledge of PEMDAS to help)

• Example. Evaluate the following expressions• A) 23

• B) (-2)3

• C) -23

• Example. Evaluate the following.

• A) -162

• B) 63

• C) -25

• D) (-2)5

• Not all exponents are the same! Always be aware of the negative sign– It’s like a “-1”– Using multiplication after exponents

• Example. Evaluate -4p2 + 4p – 2 if p = 2.

• Example. Evaluate 2x2 + 2x – 1 if x = -2.

• Assignment• Pg. 12• 15-19 odd, 21-27 odd, 33-39 odd, 48, 50, 54