1. MTH 10905 Algebra COMBINING LIKE TERMS CHAPTER 2 SECTION 1

2. Variables are the letters or symbols that represent numbers and are used when different numbers can be used in a situation.  EXP: x, y, zEXP: ☼, ☺, ♥ Expression or Algebraic Expression is the collection of numbers, variables, grouping symbols, and operation symbols.  EXP: 5EXP: 2x – 3y – 5  EXP: x 2 – 3 EXP: 3(x + 7) + 2  EXP: (x + 3) 4 Identify Terms

3. Terms are the parts that are added together.  EXP: 5x – 8y – 2EXP:2(x – 4) – 7x + 3 5x + (-8y) + (-2)2(x - 4) + (-7x) + 3 3 terms: 5x, -8y, -2 2(x - 4), -7x, 3  It is important that you list the minus sign when identifying a term.  In the Language of Mathematics we often assume that readers know certain things by the absence of a symbol. Example: 5x is assumed to have a positive sign associated with it because no sign is given. Terms

4. Numerical Coefficient or Coefficient is the number part of the term.  EXP: 6x6 is the coefficient  EXP:5(x – 2)5 is the coefficient The variable is multiplied by the coefficient Variables are used when different numbers can be used in a situation. Numerical Coefficient

5. When a variable has no coefficient we assume it is 1.  EXP: x = 1xEXP:x 2 = 1x 2  EXP:(x + 3) = 1(x + 3)EXP:ab = 1ab Constant term or constant is the term that has no variable and are used when only one number can be used in a situation. EXP: If you are charged a monthly fee of $9.95 for internet service and an hourly fee of $1.25. You charges are represented by a constant $9.95 and a variable $1.25x. 1.25x + 9.95 Like Terms or Similar Term are terms that have the same variables with the same exponents. Constants are also like terms. Identify Terms

6. Like Terms EXP: 3x and -6x2y and 8y 2x 2 and -3x 2 4ab and 5ab 3 and 42(x + 1) and -6(x + 1) Identify any like terms EXP: 6a 2 + 7a + 5a 2 Like terms: 6a 2 and 5a 2 EXP: 9 – 3x + 8x – 11 Like terms: 9 and -11 ; -3x and 8x Identify Terms

7. Identify Like Terms: EXP: 6a + 7b + 5Like terms: None EXP: 9 – 3x + 8x – 11 Like terms: 9 and -11 ; -3x and 8x Combine Like Terms means to add or subtract the like terms in an expression. 1. Determine which terms are alike 2. Add or subtract the coefficients of the like terms 3. Multiply the number found in step 2 by the common variables Like Terms

8. EXP: 6x + 7x = 13x To make math expression more real for you replacement the variable with a word such as cookies. Then you would have 6 cookies + 7 cookies = 13 cookies You can also relate the addition to the distributive property. 6x + 7x = (6 + 7)x EXP: Combine Like Terms

9. EXP:3.72a – 8.12a = (3.72 – 8.12)a = 4.40a EXP:2x + x + 10 = 2x + 1x + 10 = (2 + 1)x + 10 = 3x + 10 When writing your answers we generally list the terms that contain variables in alphabetical order from left to right, and the constant as the last term. The commutative property, a + b = b + a, and the associative property, (a + b) + c = a + (b + c), of addition allows us to rearrange the terms. EXP:7b + 9c – 12 + 5c = 7b + 9c + 5c – 12 7b + (9 + 5)c – 12 = 7b + 14c – 12 Combine Like Terms

10. EXP:-5x 2 + 7y – 3x 2 – 9 – 2y + 4 -5x 2 – 3x 2 + 7y – 2y – 9 + 4 (-5 + -3) x 2 + (7 – 2)y + (-9 + 4) -8x 2 + 5y – 5 Understanding Subtraction of Real Number will help us understand the use of the distributive property. a – b = a + (-b) Distributive property is used to remove parentheses a(b + c) = ab + ac How can you simplify using the distributive property? Distributive Property

11. EXP:6(x + 2) = 6x + (6)(2) = 6x + 12 EXP:-4(r + 3) = -4r + (-4)(3) = -4x – 12 EXP:8(w – 7) = 8w + (8)(-7) = 8w – 56 EXP:-3(r – 9) = -3r + (-3)(-9) = -3r + 27 EXP: Can the distributive property be used when we have 3 terms? Distributive Property

12. Remember that the distributive property can be expanded to more than two terms. EXP: -4(2x + 3y -5z) (-4)(2x) + (-4)(3y) + (-4)(-5z) -8x – 12y + 20z The distributive property can also be used from the right. EXP:(3a – 4b)2 (2)(3a) + (2)(-4b) 6a – 8b Distributive Property

13. Removing parentheses when they are preceded by a plus or minus sign using the distributive property When no sign or plus sign before the parentheses we simply remove the parentheses. EXP: (2x + 4)Coefficient is assumed to be 1(2x + 4) (1)(2x) + (1)(4) 2x + 4 EXP:(x + 5) x + 5 Parentheses

14. When a minus sign comes before the parentheses, all of the signs within the parentheses changes EXP: -(3x + 2) -1(3x + 2) (-1)(3x) + (-1)(2) -3x – 2 EXP:-(x + 4) -x – 5 Parentheses

15. Simplifying an expresstion 1. Use the distributive property to remove the parentheses 2. Combine like terms EXP:8 – (3x + 7) 8 + (-3x) + (-7) 8 – 3x – 7 -3x + 8 – 7 -3x +1 Simplify an Expression

16. EXP:6(5x – 3) – 2(y – 4) – 8x (6)(5x) + (6)(-3) + (-2y) + (-2)(-4) – 8x 30x – 18 – 2y + 8 – 8x 30x – 8x – 2y – 18 + 8 22x – 2y – 10 Remember there is more than one way to write a solution. However if we all use the same style it helps us compare our solutions Simplify an Expression

17. EXP: Simplify an Expression

18. EXP: Simplify an Expression

19. HOMEWORK 2.1 Page 103 – 104 #9, 11, 18, 21, 47, 59, 64, 74, 79, 93, 97, 117, 121