Math 017 Materials With Exercises

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$Math 171 Review for the Final Exam$

$Math 171 Test 2$

$MATH 171 SYLLABUS$

Lesson 5__________________________________________________________________________________Topics: Multiplication of algebraic expressions; The Distributive Law; Factorization of a commonfactor; Factorization of 1; Simplification of algebraic fractions with the use of factorization.__________________________________________________________________________________This section is about the Distributive Law, the law that relates addition to multiplication. In manycases, it allows us to rewrite the product of expressions as a sum or the sum of expression as a product.The Distributive LawIf 5 girls and 7 boys get 2 cookies each, then the girls get 2 5 10cookies, the boys get 27 14cookies, so the total number of cookies they all receive is25 271014 24Alternatively, one can find the number of cookies by adding the number of girls and boys first,5 7 12and then since each of the children gets 2 cookies, together they get2(5 7) 212 24This property is called The Distributive Law. In general,The Distributive Lawa(b c) ab aca(b c) ab acTo remove parentheses from the expression of the formfactor outside parentheses by each term inside parentheses.a(b + c) or a(b − c), multiply theExample 5.1 Use the Distributive Law to remove parentheses in the following expressions.2a) x(2 x )b) ( x 2y)c) a( b c d)Solution:2212a) x( 2 x ) x 2 x x 2x x3 2x xb) ( x 2y) 1( x 2y) 1x 12y x 2yc) The expression inside the parentheses should be treated not as a sum of threeterms but as a sum of two ( b c)and d , that is b c d ( b c) d . We can thenapply the Distributive Law a(b c d) a((b c) d) a(b c) adIf we apply the Distributive Law once again, this time to a( b c), we geta( b c d) a((b c) d) a(b c) ad ab ac ad .Thus a( b c d) ab ac ad .50
The Distributive Law applied to the product of two sumsWe can apply the Distributive Law to remove parentheses in the product of two sums ( x y)(b c).We need to look at this expression as a sum of two terms in parentheses ( b c)multiplied by theexpression ( x y). In other words, ( x y)„plays the role of a ‟ in the Distributive Law. We mayreplace a in the Distributive Law with ( x y).( x y)(b c) ( x y)b ( x y)cIf we now apply The Distributive Law to ( x y)band ( x y)c, we obtain( x y)(b c) ( x y)b ( x y)c xb yb xc ycThus the following is true.The Distributive LawFor The Product of Two Sums( x y)(b c) xb xc yb ycTo multiply two sums, you need to multiply each term of the first sum by each term of the secondone and then add all the products.Please recall, that terms can be rearranged so, equivalently, we can write( x y)(b c) xb yb xc yc .Any other order of terms would be also correct.Example 5.2 Write an equivalent expression without parentheses.a) ( a b)(2a 3)b) 3x 12xc) ( x 3y z)d) ( b c d e)ae) ( a b)(c d)(e f )Solution:a) Use the Distributive Law for product of two sums.2( a b)(2a 3) a(2a) a(3) b(2a) b(3) 2a 3a 2ab 3bb) Apply the Distributive Law. The order of factors can be changed, and thus3x 12x 2x3x1 2x(3x) (2x)1 6x2 2xc) A minus sign in front of parentheses is equivalent to multiplication by 1 ( x 3y z) ( 1)(x 3y z) 1x1(3y)1(z) x 3y zd) Each term inside parentheses must be multiplied by a .( b c d e)a ba ca da eae) Multiply ( a b)(c d), then the result must be multiplied by ( e f ) .( a b)(c d)(e f ) ( ac ad bc bd)(e f ) ace ade bce bde acf adf bcf bdf51
Page 1 and 2: Math 017MaterialsWithExercises
Page 3 and 4: TABLE OF CONTENTSLesson 1Variables
Page 5 and 6: Lesson 1___________________________
Page 7 and 8: e) „minus x ‟ or „the opposit
Page 9 and 10: For example,Evaluate 5 x when x 10
Page 11 and 12: 3xd) x( y)e) 2f) 2x yz w(t)Ex.4 T
Page 13 and 14: Ex.16 Let x 3. Rewrite the express
Page 15 and 16: e) x5f) x2Ex.28 Substitute“undefi
Page 17 and 18: Lesson 2___________________________
Page 19: Solution:Please, notice the use of
Page 22 and 23: g)i)4( a 2)h)8y (x)4(ab)j) ( a d)
Page 24 and 25: 1 2Ex.19 If possible, evaluate when
Page 26 and 27: Lesson 3___________________________
Page 28 and 29: Commutative Propertyof Additionx y
Page 30 and 31: 2 x 2 xFor example, and thus als
Page 32 and 33: Example 3.10 Determine which of the
Page 34 and 35: Exercises with Answers (For answers
Page 36 and 37: Ex.16 Write the following expressio
Page 38 and 39: s) ( 0.2xy)( 0.3z)t)4x1Ex.24 Is 1
Page 40 and 41: Lesson 4___________________________
Page 42 and 43: Numerical coefficientsNumerical Coe
Page 44 and 45: For your convenience, we will displ
Page 46 and 47: 9 818081a) 9 98097 6 76134 4 4 4
Page 48 and 49: Ex.8Simplify by raising to the indi
Page 50 and 51: 73a 2xxi) 2aj)2( 42a)x(3xk)4x2 ) 3
Page 54 and 55: FactorizationThe Distributive Law l
Page 56 and 57: Simplification of algebraic fractio
Page 58 and 59: Mistake 5.1When factoring 3 from 3x
Page 60 and 61: Ex.13 Factor2a) 5 a from the follow
Page 62 and 63: 24x ( 5x)g)xa bi)7(a b)bc ( b e)
Page 64 and 65: Adding and subtracting like termsIf
Page 66 and 67: ) This should be written as 4x 2
Page 68 and 69: Ex.4 Circle all terms that are like
Page 70 and 71: 682 122k) 6 ( d a) a dl) 3a1(4a
Page 72 and 73: Lesson 7___________________________
Page 74 and 75: For instance, the area of a rectang
Page 76 and 77: a) a b 2bc) a bd) ae)b)aba 22a a
Page 78 and 79: Ex.24 Express the expressiona) m s
Page 80 and 81: A solution, the solution set, and w
Page 82 and 83: ■ Solve the following equation 3x
Page 84 and 85: sides (subtracting 4 x from both si
Page 86 and 87: Mistake 8.2While solving an equatio
Page 88 and 89: Ex.12 Determine whether the followi
Page 90: Lesson 9___________________________
Page 94 and 95: xy x 1 yFactor x .x( y 1)1yDivide
Page 96 and 97: a) b b) a c) tEx.15. SolveEx.16. So
Page 98 and 99: For each number you should check if
Page 100 and 101: ■ Solve the inequality 4x 9 1.
Page 102 and 103:
■ Solve the following inequality
Page 104 and 105:
Ex.10 Graph the following number se
Page 106 and 107:
d) z 3e) z 13 Ex.22 Knowing x 1
Page 108 and 109:
Example 11.2 The expression( 22 2x
Page 110 and 111:
Solution:a) To match the form y mx
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a x and b 3 , so now we can rewri
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Ex.9 For each of the following expr
Page 116 and 117:
114xc) y 5d) y 3x 2 0e) 3y 6x1f
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APPENDIX A:Lesson 1ANSWERS TO EXERC
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49C 3255 2(L+W)62mc75a) a b expon
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3(m n)a(x1)g)h)2tx19s s s sThe opp
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52233x1 2 x5 3 1513 a) m ( 2m) 2mb
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c) Numerator: one term, 3ab (with t
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18 a) 9 b) 3 c) 3 d) 3e) 6 f) 279
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11 a) x 1 b)12 a) x abcx a b42 b
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c) x 2d) a 7e) x 10f) a 225 a)
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x or 4x ( 7) 0; a 4; b 7g) x (
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3. Let m = ─3. Evaluate the follo
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1. Write the following statements a
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6. Solve the following equations:8.
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8. Factor the following expressions
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___________________________________
Page 146:
3 ;b) x 3 y 6 xy 2 A xy 28. a) x
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Math 017 Materials With Exercises

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