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Algebra 2 A Chapter 1 Section 1 Algebraic Expressions And Formulas Algebraic Expressions ALGEBRA 2 LESSON 1-1 Use the order of operations to simplify each expression. 1. 8 • 3 – 2 • 4 2. 8 – 4 + 6 ÷ 3 3. 24 ÷ 12 • 4 ÷ 3 4. 3 • 82 + 12 ÷ 4 5. 27 + 18 ÷ 9 – 32 + 1 6. (40 + 24) ÷ 8 – (23 + 1) Algebraic Expressions ALGEBRA 2 LESSON 1-1 Solutions 1. 8 • 3 – 2 • 4 = (8 • 3) – (2 • 4) = 24 – 8 = 16 2. 8 – 4 + 6 ÷ 3 = 8 – 4 + (6 ÷ 3) = 8 – 4 + 2 = (8 – 4) + 2 = 4 + 2 = 6 3. 24 ÷ 12 • 4 ÷ 3 = (24 ÷ 12) • 4 ÷ 3 = 2 • 4 ÷ 3 = (2 • 4) ÷ 3 = 8 ÷ 3 = 8 or 2 2 3 3 4. 3 • 82 + 12 ÷ 4 = 3 • 64 + 12 ÷ 4 + (3 • 64) + (12 ÷ 4) = 192 + 3 = 195 5. 27 + 18 ÷ 9 – 32 + 1 = 27 + 18 ÷ 9 – 9 + 1 = 27 + (18 ÷ 9) – 9 + 1 = 27 + 2 – 9 + 1 = (27 + 2) – 9 + 1 = 29 – 9 + 1 = (29 – 9) + 1 = 20 + 1 = 21 6. (40 + 24) ÷ 8 – (23 + 1) = (40 + 24) ÷ 8 – (8 + 1) = 64 ÷ 8 – 9 = (64 ÷ 8) – 9 = 8 – 9 = –1 Evaluating Algebraic Expressions Variable – a symbol, usually a lowercase letter, that represents one or more numbers Algebraic expression or variable expression – a mathematical phrase that can include numbers, variables, and operation symbols Evaluating or Simplifying an expression means substituting numbers for variables and following the order of operations Evaluating Algebraic Expressions Polynomial – a monomial or sum of monomials Term – the monomials that makes up the polynomial Binomial – 2 unlike terms Trinomial – 3 unlike terms Like Term example: 2x and 5x Evaluate a-2b+ab for a=3 and b=-1 Example 1 a 2b ab 3 2(1) 3(1) 3 (2) (3) 3 2 ( 3) 5 ( 3) 2 Substitute 3 for a and -1 for b Multiply First To subtract, add the opposite Add from left to right Add Try These Problems Evaluate each expression for x = 4 and y = -2 a) x + y ÷ x a) 4 + (-2) ÷ 4 = 4 + (-1/2) = 3 ½ = 7/2 = 3.5 3x – 4y + x – y b) a) 3(4) – 4(-2) + 4 – (-2) = 12 – (-8) + 4 –(-2) = 20 + 4 – (-2) = 24 – (-2) = 26 x + 2x ÷ y – 2y c) a) 4 + 2(4) ÷ (-2) – 2(-2) = 4 + 8 ÷ (-2) – 2(-2) = 4 + (-4) -2(-2) = 4 + (-4) +4 = 4 Evaluate –x2-2(x+1) for x=3 Example 2 -x2 – 2 (x + 1) = -(3)2 – 2 (3 + 1) Substitute 3 for x. = -9 – 2(4) Simplify the power and the parenthesis. = -9 – 8 Multiply = -17 Subtract Try These Problems Evaluate each expression for c = -3 and d = 5. a) c2 – d2 a) (-3)2 – 52 = 9 – 25 = -16 c(3 - d) – c2 b) a) (-3)(3 – 5) – (-3)2 = (-3)(-2) – 9 = 6 – 9 = -3 -d2 – 4(d – 2c) c) a) -(52) – 4(5 – 2(-3)) = -25 – 4(5 +6) = -25 – 4(11) = -25 -44 = -69 Real World Connection ALGEBRA 2 LESSON 1-1 The expression –0.08y 2 + 3y models the percent increase of Hispanic voters in a town from 1990 to 2000. In the expression, y represents the number of years since 1990. Find the approximate percent of increase of Hispanic voters by 1998. Since 1998 – 1990 = 8, y = 8 represents the year 1998. –0.08y2 + 3y = –0.08(8)2 + 3(8) Substitute 8 for y 19 The number of Hispanic voters had increased by about 19%. Real World Connection ALGEBRA 2 LESSON 1-1 Click here to go to page 9 examples on line