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Question

Take away:

(i) 65x245x3+56+32x from x3352x2+35x+14

(ii) 5a22+3a32+a365 from 13a334a252

(iii) 74x3+35x2+12x+92 from 72x3x25

(iv) y33+73y2+12y+12 from 1353y2

(v) 23ac57ab+23bc from 32ab74ac56bc

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Solution

(i) 65x245x3+56+32x from x3352x2+35x+14=(x3352x2+35x+14)(65x245x3+56+32x)=x3352x2+35x+1465x2+45x35632x=x33+45x352x265x2+35x32x+1456=(13+45)x3+(5265)x2+(3532)x+(1456)=5+1215x3+251210x2+61510x+31012=1715x33710x2910x712

(ii) 5a22+3a32+a365 from 13a334a252=(13a334a252)(5a22+3a32+a365)=13a334a25252a232a3a3+65=13a332a334a252a2a3+6552=(1332)a3(34+52)a2(13)a+(6552)=296a33+104a213a+122510=76a3134a213a1310

(iii) 74x3+35x2+12x+92 from 72x3x25=(72x3x25)(74x3+35x2+12x+92)=72x3x2574x335x212x92=74x3x2535x2x312x+7292=74x3(15+35)x2(13+12)x+792=74x31+35x22+36x22=74x345x256x1

(iv) y33+73y2+12y+12 from 1353y2=(1353y2)(y33+73y2+12y+12)=1353y2y3373y212y12=y33(53+73)y212y12+13=y335+73y212y326=y33123y212y16=13y34y212y16

(v) 23ac57ab+23bc from 32ab74ac56bc=(32ab74ac56bc)(23ac57ab+23bc)=32ab74ac56bc23ac+57ab23bc=32ab+57ab56bc23bc74ac23ac=(32+57)ab(56+23)bc(74+23)ac=21+1014ab5+46bc21+812ac=3114ab96bc2912ac=3114ab32bc2912ac


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