Algebra 1 Notes Warm Up 1. If y = 16, y – 3.6 = ____ 3. = ____ 2. 45 – (- 14) = ___ 4. -3 + 17 = ____ 12.4 14 16 – 3.6 59 14 GOAL USE THE DIST. PROP. TO EVALUATE/SIMPLIFY EXPRESSIONS; RECOGNIZE AND USE THE COMMUTATIVE AND ASSOCIATIVE PROP.; FIND SQUARE ROOTS; CLASSIFY AND ORDER REAL NUMBERS. KEY WORDS & PROPERTIES COEFFICIENT, EQUIVALENT EXPRESSIONS, IRRATIONAL NUMBERS, LIKE TERMS, PERFECT SQUARE, PRINCIPAL SQUARE ROOT, RADICAL SIGN, RATIONAL APPROXIMATION, REAL NUMBERS, SIMPLEST FORM, SQUARE ROOT, TERM,

Properties Commutative Associative Distributive Identity Order of the terms does not change your answer 3 + 5 = 5 + 3 a + b = b + a 4 * 3 = 3 * 4 x * y = y * x Moving grouping symbols does not change your answer 3 + (5 + 7) = (3 + 5) + 7 (6 * 5) * 9 = 6 * (5 * 9) a + (b + c) = (a + b) + c a * (b * c) = (a * b) * c Multiply your outside term times all terms inside the parentheses a(b + c) = ab + ac 5(7 + 9) = 5(7) + 5(9) Of Addition: 3 + 0 = 3 x + 0 = x Of Multiplication: 5 * 1 = 5 x * 1 = x

Example 1 Use the Distributive Property to simplify the expressions.  3(2x + 6)     5(6m + 4n – 3n)

Example 2 Use the distributive property to write this product in another way.

Simplify by collecting like terms. Example 3 Simplify by collecting like terms.

Example 4 Simplify. 3.2(x + y) + 2.3(x + y) + 4x

Example 5 Evaluate.