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Algebra 1 Notes Warm Up 1. 12.4 If y = 16, y – 3.6 = ____ 16 – 3.6 2. 59 45 – (- 14) = ___ 3. 36 4(2) 2 14 = ____ 14 4. -3 + 17 = ____ 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 Order of the terms does not change your answer 3+5=5+3 a+b=b+a 4*3=3*4 • Associative • Distributive • Identity 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 Of Multiplication: 5 * 1 = 5 x+0=x x*1=x Example 1 Use the Distributive Property to simplify the expressions. 3(2x + 6) 5(6m + 4n – 3n) 3(2x) 3(6) 5(6m ) 5(4n) 5(3n) 6x 18 30 m 20 n 15 n 30 m 5n Example 2 Use the distributive property to write this product in another way. 1 18( 2 ) 9 1 18(2) 18( ) 9 36 2 38 Example 3 Simplify by collecting like terms. 3 3 4a 6a 3a 8a 3 3 4a 3a 6a 8a 7a3 14a Example 4 Simplify. 3.2(x + y) + 2.3(x + y) + 4x 3.2x 3.2y 2.3x 2.3y 4x 3.2x 2.3x 4x 3.2y 2.3y 9.5x 5.5y Example 5 Evaluate. 94 9.695