[15] Factorization

2007-12-31 8:50 pm
1. 1+x-y-xy
2. aw+bw+a+b
3. cx+cy-y-x
4. ac+bc-ad-bd
5. 2p+ap+2q+aq
6. ku-kv+3v-3u
7. xy-ay+2x-2a
8. 6x-ax-6y+ay
9. st-3s-2t+6

回答 (2)

2008-01-01 6:07 am
1.(1+x)(1-y)
2.(a+b)(w+1)
3.(x+y)(c-1)
4.(a+b)(c-d)
5.(2+a)(p+q)
6.(u-v)(k-3)
7.(y+2)(x-a)
8.(6-a)(x-y)
9.(t-3)(s-2)
參考: 富有實力的人
2007-12-31 9:06 pm
1. 1+x-y-xy
= 1-y+x-xy
= (1-y)+x(1-y)
=(1+x)(1-y)

2. aw+bw+a+b
= aw+a+bw+b
= a(w+1)+ b(w+1)
= (a+b)(w+1)

3. cx+cy-y-x
= cx-x+cy-y
= x(c-1)+y(c-1)
= (x+y)(c-1)

4. ac+bc-ad-bd
= ac-ad+bc-bd
= a(c-d)+b(c-d)
= (a+b)(c-d)

5. 2p+ap+2q+aq
= p(2+a)+q(2+a)
= (p+q)(2+a)

6. ku-kv+3v-3u
= ku-3u-kv+3v
= u(k-3)-v(k-3)
= (u-v)(k-3)

7.xy-ay+2x-2a
= y(x-a)+2(x-a)
= (y+2)(x-a)

8. 6x-ax-6y+ay
= 6x-6y-ax+ay
= 6(x-y)-a(x-y)
= (6-a)(x-y)

9. st-3s-2t+6
= s(t-3)-2(t-3)
= (s-2)(t-3)

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