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MTH 10905 Algebra

MTH 10905 Algebra. Combining Like Terms CHAPTER 2 Section 1. Identify Terms. Variables are the letters or symbols that represent numbers and are used when different numbers can be used in a situation. EXP: x, y, z EXP: ☼ , ☺ , ♥

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MTH 10905 Algebra

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  1. MTH 10905Algebra Combining Like Terms CHAPTER 2 Section 1

  2. Identify Terms • Variables are the letters or symbols that represent numbers and are used when different numbers can be used in a situation. • EXP: x, y, z EXP: ☼ , ☺ , ♥ • Expression or Algebraic Expression is the collection of numbers, variables, grouping symbols, and operation symbols. • EXP: 5 EXP: 2x – 3y – 5 • EXP: x2 – 3 EXP: 3(x + 7) + 2 • EXP: (x + 3) 4

  3. Terms • Terms are the parts that are added together. • EXP: 5x – 8y – 2 EXP: 2(x – 4) – 7x + 3 5x + (-8y) + (-2) 2(x - 4) + (-7x) + 3 3 terms: 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.

  4. Numerical Coefficient • Numerical CoefficientorCoefficientis the number part of the term. • EXP: 6x 6 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.

  5. Identify Terms • When a variable has no coefficient we assume it is 1. • EXP: x = 1x EXP: x2 = 1x2 • 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.

  6. Identify Terms • Like Terms EXP: 3x and -6x 2y and 8y 2x2 and -3x2 4ab and 5ab 3 and 4 2(x + 1) and -6(x + 1) • Identify any like terms EXP: 6a2 + 7a + 5a2 Like terms: 6a2 and 5a2 EXP: 9 – 3x + 8x – 11 Like terms: 9 and -11 ; -3x and 8x

  7. Like Terms • Identify Like Terms: EXP: 6a + 7b + 5 Like 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. • Determine which terms are alike • Add or subtract the coefficients of the like terms • Multiply the number found in step 2 by the common variables

  8. Combine Like Terms • 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:

  9. Combine Like Terms • 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 – 1 2 7b + (9 + 5)c – 12 = 7b + 14c – 12

  10. Distributive Property • EXP: -5x2 + 7y – 3x2 – 9 – 2y + 4 -5x2 – 3x2 + 7y – 2y – 9 + 4 (-5 + -3) x2 + (7 – 2)y + (-9 + 4) -8x2 + 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?

  11. Distributive Property 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?

  12. Distributive Property • 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

  13. Parentheses • 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

  14. Parentheses • 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

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

  16. Simplify an Expression 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

  17. Simplify an Expression EXP:

  18. Simplify an Expression EXP:

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

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