BYDR. IRENE P. SOLANO

REVIEW OF ALGEBRA(Business Math 2)

LAWS OF SIGNED NUMBERSI. ADDITIONA. LIKE SIGNS – FIND THE SUM OF THEIR

ABSOLUTE VALUES AND PREFIX THE COMMON SIGN

B. UNLIKE SIGNS – FIND THE DIFFERENCE OF THEIR ABSOLUTE VALUES AND PREFIX THE SIGN OF THE GREATER ABSOLUTE VALUE

LEARNING OBJECTIVESAT THE END OF THIS SESSION, STUDENTS

SHOULD BE ABLE TO1.EXPLAIN THE BASIC LAWS OF ALGEBRA2.PERFORM THE REQUIRED OPERATIONS3.APPRECIATE THE KNOWLEDGE AND SKILLS

ACQUIRED

II. SUBTRACTION CHANGE THE SIGN OF THE SUBTRAHEND (THE NUMBER BEING SUBTRACTED) THEN FOLLOW THE RULES OF ADDITION OF SIGNED NUMBERS

III. MULTIPLICATION A. LIKE SIGNS – PRODUCT IS POSITIVE

B. UNLIKE SIGNS – PRODUCT IS NEGATIVE

IV. DIVISIONA. LIKE SIGNS – QUOTIENT IS POSITIVEB. UNLIKE SIGNS – QUOTIENT IS NEGATIVE

EXERCISE

1) (-2) + (3) – (5)

2) (-5)2

3) (12) + (-3)

4) (2) (-3) – (-1)2 + 10

5) (-6) ÷ (2) + (-2) (-7)

6) 12 ÷ 3 + 2 (-1)

7) 10 – (10 ÷ 2) + (-5) (2)

SIMILAR & DISSIMILAR TERMSSIMILAR TERMS – HAVE THE SAME LITERAL

COEFFICIENTSDISSIMILAR TERMS – HAVE DIFFERENT

LITERAL COEFFICIENTSONLY SIMILAR TERMS CAN BE ADDEDTO ADD SIMILAR TERMS, FIND THE

ALGEBRAIC SUM OF THE NUMERICAL COEFFICIENTS AND COPY THE LITERAL PARTS

EXERCISE

1) 4c – d + 6c + 2d

2) 8mn – 9n – 10mn

3) 3x2 + 2x – x2 – 5x – 3x2

4) 6x – y + 12x – 2y

MULTIPLICATION OF MONOMIALSFIND THE PRODUCT OF THEIR NUMERICAL

COEFFICIENTS AND ADD THE EXPONENTS OF THE SAME BASE

EXAMPLES1) (3x3) (-2x2) = - 6x5

2) (3ab) (5by) = 15ab2y

DIVISION OF MONOMIALSFIND THE QUOTIENT OF THEIR NUMERICAL

COEFFICIENTS AND SUBTRACT THE EXPONENTS OF THE SAME BASE

EXAMPLES1)(-8m5) ÷ (4m2) = -2m2) (12ab) ÷ (4a) = 3b

THE PRODUCT OF A MONOMIAL AND A POLYNOMIALUSE DISTRIBUTIVE PROPERTY OF

MULTIPLICATIONEXAMPLES

1) x (y + z) = xy + xz2) a2 (b – 3c + d) = a2 b – 3 a2 c + a2 d

EXERCISE

1) 3 (a + b) + 8 (a + b)

2) (-7y5) (5y6)

3) 3x2

4) 36a2 ÷ (-6a)

5)

6

4x

63

xx

THE PRODUCT OF POLYNOMIALSAPPLY THE DISTRIBUTIVE PROPERTY OF

MULTIPLICATION (MULTIPLY EACH TERM IN THE MULTIPLIER BY EACH TERM IN THE MULTIPLICAND)

EXAMPLES1) (a+b) (x+y) = a (x +y) + b (x+y) = ax+ay+bx+by2) (a-b) (x+y+z) = a(x+y+z)-b(x+y+z)

= ax +ay +az –bx –by -bz

SPECIAL PRODUCTSI. FOIL (First Outer + Inner Last)

MULTIPLY THE FIRST TWO TERMSADD THE PRODUCT OF THE MIDDLE TERMS OR INNER TERMS TO THE PRODUCT OF THE END TERMS THEN MULTIPLY THE TWO SECOND TERMS OF THE BINOMIAL

Exercise1) (3 – 2x) (2 + 5x)

2) (7x – a ) (x – 2a)

II. THE SQUARE OF A BINOMIALa) Square the first termb) Find twice the product of the first and second termc) Square the second term

Note that the square of a binomial is a perfect square trinomial

Exercise1) (2x – y)2

2) (x – 3m)2

III. PRODUCT OF SUM AND DIFFERENCE OF TWO TERMS

The product of the sum and difference of two terms = difference of two squares

(x + y) (x – y) = x2 – y2

EXERCISE1) (10 – x) (10 + x)

2) (x2 – 3) (x2 + 3)

FACTORING POLYNOMIALSI. COMMON FACTORS

Find the common factor and divide each term in the polynomial by the greatest common factor, then write the quotients inside a parenthesis

Exercise1) 2x + x2

2) 3x3 + 6x2 + 9x

II. FACTORING QUADRATIC TRINOMIALS a) Factor the first termb) Factor the last term such that the algebraic sum of the products of the inner terms and outer terms in the binomials is equal to the middle term in the trinomial

Exercise1) x2 + 4x – 12

2) 9 + 24x + 16x2

III. FACTORING THE DIFFERENCE OF TWO SQUARESThe factors of a difference of two squares are two binomials which are sum and difference of their square roots

EXERCISE1) 9 – a2

2) 4a2 - 121

IV. FACTORING BY GROUPING a) Group the terms with common factor b) Put out the common factor of each group c) Factor further by finding the common factors

EXERCISE1) ax – ay – by + bx

2) x3 – 2x2 + 4x - 8

EVALUATIONI. Find each of the following products:1) (m – 2a) (2m – a)2) (3x – ab)2

3) (3x + 10y2 ) (3x – 10y2 ) II. Find the factors of each of the following:1) 9ax – 6x2ay + 3ax3

2) 9x2 + 6x + 13) 100 – b2y2 4) 2x2 + 10 x - 485) y3 – 2y2 + 5y - 10

REFERENCEQUANTITATIVE TECHNIQUES FOR BUSINESS

MANAGEMENT- BY PRAXEDES SOLINA VICTORIANO

REMINDERSTUDY LINEAR EQUATIONS AND LINEAR

INEQUALITIESOTHER AVAILABLE REFERENCES IN OUR

CBEA READING CENTER ARE THE FFG1)QUANTITATIVE TECHNIQUES FOR BUSINESS

(WITH CASE ANALYSIS AND COMPUTER APPLICATION) BY DEVEZA, HOWE, COPO, ARCE, ALTARES, ARAO, ET. AL.

2) QUANTITATIVE TECHNIQUES IN DECISION MAKING BY DR. ERLINDA AGUAVIVA