 # MODULAR-TOOL-M-101-PRELIM-PERIOD.docx - College of Teacher...

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College of Teacher Education2ndSemester A.Y. 2021-2022MODULAR TOPICS IN M-101 (PRELIM PERIOD)MODULE 1 .BINOMIAL THEOREMAPPLICABLE FORMULASA.PASCALTRIANGLE1(x+y)0=111(x+y)1=x + y121(x + y)2= x2+ 2xy + y21331(x + y)3= x3+ 3x2y + 3xy2+ y314641.........15101051(x+y)5= x5+ 5x4y + 10x3y2+ 10x2y3+ 5xy4+ y5B.BINOMIAL THEOREM FORMULA(x + y)n=xno!+nxn−1y11!+n(n−1)xn−2y22!+n(n−1)(n−2)xn−3y33!+ ……+ ……+ynExample.(x + y)3=x30!+3x31y11!+3.2x32y22!+y3(x +y)3=x31+3x2y1+6x y22+ y3(x+y¿¿3=x3+ 3x2y + 3xy2+ y3C.COMBINATORIAL EXPANSION FORMULA(x+y)n=nCo❑❑xn--0+ n C1xn-1y1+ n C2xn - 2y2+ …………….. + n C n xn - nynNote that n C r =n!r!(n−r)!or you may use your calculatorExample. ( x + y)5=5C0x5 - 0+5C1x5 - 1y1+ 5C2x5 - 2y2+ 5C3x5 - 3y3+ 5C4x5 - 4y4+ 5C5x5 - 5y5( x + y)5= 1 x5+5 x4y + 10 x3y2+ 10 x2y3+ 5 x y4+ 1 x0y5( x+y)5=x5+ 5 x4y + 10 x3y2+ 10 x2y3+ 5 x y4+ y5Assignment/Student ActivityShow the complete and detailed solution.1. Using Pascal Triangle, evaluate and simplify the followinga) ( x + y)6b)( 2x - 3y)42. Using the Binomial Theorem Formula, evaluate and simplify the followinga) ( x -y )4b)( 3a + 4b)53. Using Combinatorial Expansion Formula, evaluate and simplify the following.a) (2p + 3q)4b)(3m - 5n)6
ADDITIONAL EXAMPLES1.Using PASCAL TRIANGLENote: The signs are alternately changing from + to - if the binomial form is ( x - y )nand the signs are all + if the binomial form is (x + y)n.

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