1.ab(c2-d2)-(a2-b2)cd
=abc²-abd²-a²cd+b²cd
=abc²-a²cd+b²cd-abd²
=ac(bc-ad)+bd(bc-ad)
=(ac+bd)(bc-ad)
2.(a+b)2+(a+c)2-(c+d)2-(b+d)2
=(a+b)2-(c+d)2+(a+c)2-(b+d)2
=(a+b+c+d)(a+b-c-d)+(a+b+c+d)(a+c-b-d)
=2(a+b+c+d)(a+d)
3.解方程2x的三次方-3x2-8x-3=0
2x²(x-3)+3x²-8x-3=02x²(x-3)+(3x+1)(x-3)=0 ( 2x²+3x+1)(x-3)=0 (2x+1)(x+1)(x-3)=0
(2x+1)=0x= -1/2(x+1)=0x= -1(x-3)=0 x=3 所以x1= -1/2x2= -1x3=3
4.3x2+5xy-2y2+x+9y-4
可設 3x2+5xy-2y2+x+9y-4
=（ax+by+c）(dx+ey+f)
=adx²+（ae+bd）xy+bey²+(af+ed)x+(bf+ce)y+cf
故有：ad=3ae+bd=5be= -2af+ed=1 bf+ce=9 cf= -4
解上方程組：a=1b=2 c= -1 d=3 e= -1f=4abcdef均為整數(shù),如果不會解方程組,可以用數(shù)去試.如ad=3 1*3=33*1=3 （-1）*（-3）=3（-3）*（-1）=3雖慢點可做出來.
所以：3x2+5xy-2y2+x+9y-4
=（x+2y-1）(3x-y+4)
5.4b2-10b+c2-5c+4bc+6形如（xa+yb+z）(oa+pb+q)再展開歸項列方程組
6.a2-c2+2ab+b2-d2-2cd
=.a2+2ab+b2-c2-d2-2cd
=(a+b)²-(c+d)²
=(a+b+c+d)(a+b-c-d)