1 2 Algebra 2 1 2 Algebraic Expressions

1. 2 Algebra 2 1. 2 Algebraic Expressions

1. 2 Algebraic Expression- an expression that contains one of more variables. Ex’s: 2 x - 3 z + y 3 – 2 p Term- is a number, variable, or a product of a number and one or more variables Ex’s: 4 x + 3 has two terms 4 x 2 + 3 x + 4 has three terms Coefficient- the numerical factor in a term. Ex’s: -3 k -3 is the coefficient 2 x 2 is the coefficient

1. 2 Algebra 2 Evaluate- substitute numbers for variables in the expression and then simplify the expression following the order of operations. Example: 2 x + 3 y when x = 2 and y = -1 2(2) + 3(-1) 4 + -3 = 1

1. 2 Algebra 2

Algebraic Expressions Lesson 1 -2 Algebra 2 Additional Examples Evaluate 7 x – 3 xy for x = – 2 and y = 5. 7 x – 3 xy = 7(– 2) – 3(– 2) (5) Substitute – 2 for x and 5 for y. = – 14 – (– 30) Multiply first. = – 14 + 30 To subtract, add the opposite. = 16 Add.

1. 2 Algebra 2 Evaluate each expression for x = 4 and y = - 2 1. ) x + y 2. ) 3 x – 4 y + x – y

Algebraic Expressions Lesson 1 -2 Algebra 2 Additional Examples Evaluate (k – 18)2 – 4 k for k = 6. (k – 18)2 – 4 k = (6 – 18)2 – 4(6) Substitute 6 for k. = (– 12)2 – 4(6) Subtract within parentheses. = 144 – 4(6) Simplify the power. = 144 – 24 Multiply. = 120 Subtract.

Algebraic Expressions Lesson 1 -2 Algebra 2 Additional Examples The expression – 0. 08 y 2 + 3 y 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. 08 y 2 + 3 y = – 0. 08(8)2 + 3(8) Substitute 8 for y 19 The number of Hispanic voters had increased by about 19%.

Algebraic Expressions Lesson 1 -2 Algebra 2 Additional Examples Simplify by combining like terms. 2 h – 3 k + 7(2 h – 3 k) = 2 h – 3 k + 14 h – 21 k Distributive Property = 2 h + 14 h – 3 k – 21 k Commutative Property = (2 + 14)h – (3 + 21)k Distributive Property = 16 h – 24 k

Algebraic Expressions Lesson 1 -2 Algebra 2 Additional Examples Find the perimeter of this figure. Simplify the answer. c c P = c + + d + (d – c) + d + + c + d 2 2 c c = c + 2 + d – c + d + 2 + c + d c c = + + c + 4 d 2 2 2 c = + c + 4 d 2 = c + 4 d = 2 c + 4 d

1. 2 Algebra 2