CHAPTER 5 – EXPRESSIONS Lesson 5-1: Algebraic Expressions The branch of mathematics that involve expressions with variables is called _____________. In algebra, the __________________________________ ___________ is often omitted. The numerical factor of a multiplication expression that contains a variable is called a coefficient. So, 6 is the of 6d. Example 1: Evaluate 2(n + 3) if n = -4. 2(n + 3) = 2(-4 + 3) = 2(-1) = -2 Example 2: Evaluate 8w – 2v if w = 5 and v = 3. 8w – 2v = 8(5) – 2(3) = 40 – 6 = 34 Example 3: Evaluate 4y3 + 2 if y = 3. 4y3 + 2 = 4(3)3 + 2 = 4(27) + 2 = 110 Got it? 1, 2, & 3 Evaluate each expression if c = 8 and d = -5. a. c – 3 b. 15 – c c. 3(c + d) d. 2c – 4d e. d2 – c2 f. 2d2 + 5d Example 4: Athletic trainers use the formula , where a is a person’s age, to find the minimum training heart rate. Find Latrina’s minimum training heart if she is 15 years old. = = = = 123 Latrina’s minimum training heart rate is 123 beats per minute. Got it? 4 To find the area of a triangle, use the formula , where b is the base and h is the height. What is the area in square inches of a triangle with a height of 6 inches and a base of 8 inches? To translate a verbal phrase to an algebraic expression, the first step is to define a variable. When you define a variable, you choose a variable to represent the unknown. Example 5: Marisa wants to buy a DVD player that costs $150. She already saved $25 and plans to save an additional $10 each week. Write an expression that represents the total amount of money Marissa has saved after any number of weeks. 25 + 10w represents the total saved after any number of weeks.
A is an algebraic expression in which the variables is raised to the _____ power. The table below gives some examples of expressions that are linear and some examples of expressions that are not linear. Example 1: Add. (2x + 3) + (x + 4) = 3x + 7 Example 2: Add. (2x – 1) + (x – 5). + = 3x - 6 Got it? 1 & 2 a. (3x – 5) + (2x – 3) b. (2x – 4) + (3x – 7) Example 3: Find (2x – 3) + (-x + 4). Use models. Zero pairs are two objects that together equal zero. Example 4: Find 2(x + 3) + (3x + 1) 2(x + 3) + 3x + 1 = 2 x + 2 3 + 3x + 1 = 2x + 6 + 3x + 1 = 5x + 7 Example 5: Find 5(x – 4) + (2x – 7). 5(x - 4) + 2x - 7 = 5 x + 5 (-4) + 2x - 7 = 5x + -20 + 2x - 7 = 7x – 27 Got it? 3-5 Add. Use models if needed. a. (x – 1) + (2x + 3) b. (x – 4) + (-2x + 1) c. 6(x + 7) + (x + 3) d. (12x + 19) + 2(x – 10) Example 6 Write a linear expression in simplest form to represent the perimeter of the triangle. Find the perimeter if the value of x is 5 centimeters. the linear expression for the perimeter. (3x – 3) + (2x + 9) + 5x Combine like terms. (3x + 2x + 5x) + (-3 + 9) 10x + 6 Find the perimeter. 10(5) + 6 = 56 centimeters
Example 6: A hat store tracks to sale of college and professional team hats for m months. The number of college hats sold is represented by (6m + 3). The number of professional hats sold is represented by (5m – 2). Write an expression to show how many more college hats were sold than professional hats. Then evaluate the expression if m equals 10. Find (6m + 3) – (5m – 2) 6m + 3 + (-5m) + 2 = m + 5 10 + 5 = 15. So 15 more college team hats were sold. Guided Practice: Subtract. Use models if needed. 1. (2x + 4) – (-x + 5) 2. (6x + 9) – (7x – 1) 3. The number of runs scored by the home team at a baseball game is represented by (x + 7). The number of runs scored by the visiting team is represented by (3x – 7). Write an expression to find how many more runs the home team scored than the visiting team. Then evaluate the expression if the value of x is 6. Journal: Why are you allowed to add a zero pair to any expression? Lesson 5-8: Factor Linear Expressions A monomial is a , a , or a _______________ _____ ___ __________________ and one or more variables. Monomials Not Monomials 25, x, 40x x + 4, 40x + 120 To factor a number means to write it as a product of its factors. We will use the GCF (Greatest Common Factor) to help us factor monomials Example 1: Find the GCF for 4x, 12x. 4x = 2 2 x 12x = 2 2 3 x Circle the common factors. 2 2 x = 4x The GCF of 4x and 12x is 4x Example 2: Find the GCF for 18a, 20ab. 18a = 2 3 3 a 12x = 2 2 5 a b Circle the common factors. 2 a = 2a