Algebraic Expressions

Definition of Terms Variable Algebraic Expression A symbol that represents one or more numbers, usually a letter Algebraic Expression A meaningful collection of numbers, variables and signs, positive or negative, of operations that make a mathematical and logical sense.

Definition of Terms Term Evaluate A basic unit of an algebraic expression Either a number or a product of number and one or more variables Example: -3ax Evaluate When you substitute numbers for the variables in an expression and follow the order of operation. Numerical coefficient Variables Literal coefficients

Evaluating an Algebraic Expression Evaluate each expression for the given values of the variables. 4a + 7b + 3a – 2b + 2a; a = -5 and b = 3 2. 5y – 3z + 4y – z – 3y; y = 3 and z = -2 3. -k2 – (3k – 5n) + 4n; k = -1 and n = -2 -30 26 -16

Do this… Evaluate each expression for the given values of the variables. 3y – (4y + 6x); x = 3 and y = -2 -5(x + 2y) + 15(x + 2y); x = 7 and y = -7 -d2 – 4(d – 2c) ; c = -3 and d = 5 The expression 16t2 models the distance in feet that an object falls during t seconds after being dropper. Find the distance an object falls after 2 seconds. How about after 10 seconds? -16 -70 -69 64 ft; 1600 ft

Simplifying Algebraic Expressions Properties for Simplifying Algebraic Expression Let a, b, and c represent real numbers. Definition of Subtraction a – b = a + (-b) Definition of Division a ÷ b = a/b = a• 1/b, b  0 Distributive Property for Subtraction a(b – c) = ab – ac Multiplication by zero a • 0 = 0

Properties for Simplifying Algebraic Expression Let a, b, and c represent real numbers. Multiplication by -1 -1 • a = -a Opposite of a Sum -(a + b) = -a + (-b) Opposite of a Difference -(a – b) = b – a Opposite of a Product -(ab) = -a• b = a • (-b) Opposite of an Opposite -(-a) = a

Simplify by combining like terms. 2x2 + 5x – 4x2 + x – x2 -2(r + s) – 2(2r + 2s) y(1 + y) – 3y2 – (y + 1) -3x2 + 6x -6r – 6s -2y2 – 1

Do this… Simplify by combining like terms. 6r + 3s + 2s + 4r xy + 2x + x 3(2x + 1) – 8 7b – (3a – 8b) 10r + 5s xy + 3x 6x – 5 -3a + 15b

Finding Perimeter Find the perimeter of each figure. 10x 10c + 2d 1. 2. 3c 2c d 3c – d 3 6c – 2d 3x y 2x – y 2x 3x – y 10x 10c + 2d

In-class activity Homework Do the worksheet assigned to you. Page 15 #s 36 – 37 Page 16 #s 42 – 46, 47 – 48