BM2 Algebra
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Transcript of BM2 Algebra
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