[20] Factorization

1. x2-x+(1/4)=x2-x+(1/2)2=(x- 1/2)2
2. (a2/16)+(a/2)+1=(1/16)(a2+8a+16)=(1/16)(a+4)2
3. 25x2y2-5xy+(1/4)=25x2[y2- y/(5x) + 1/(100x2)]=25x2[y2- y/(5x) +1/(10x)2]
=25x2[y- 1/(10x)]2 answer can be either of that and 25y2[x-1/(10y)]2
4. a2+2+(1/a)2=(a+ 1/a)2
5. 169(x-y)2-234(x-y)+81
Denote u=x-y
169u2-234u+81=(13u-9)2=(13x-13y-9)2
6. (a+2b)2-4(a+2b)(2a-b)+4(2a-b)2
Denote x=a+2b and y=2a-b
x2-4xy+4y2=(x-2y)2=(a+2b-4a+2b)2=(4b-3a)2
7. 2a6-24a4+72a2=2a2(a4-12a2+36)
Denote y=a2
2y(y2-12y+36)=2y(y-6)2=2a2(a2-6)2
8. 0.01u2-0.1u+0.25=(1/100)(u2-10u+25)
=(1/100)(u-5)2
9. 0.16m2‑1.2mn+2.25n2=0.16(m2-7.5mn+14.0625n2)
=0.16[m2-7.5mn+(3.75n)2]
=0.16(m-3.75n)2
10a. x2+2x+1=(x+1)2
10b. x2+2x+1-y2=(x+1)2-y2
=(x+y+1)(x-y+1)
第一次做這麼難的factorization

2008-01-03 18:29:30 補充：
沒有steps反而是最佳解答 ???

1=X+1/4
wait a min