2.(x-2y)^2-9a-54ay-81y^2
3.4x^2-36z^2-28xy+49y^2
4.p^2+6pq+9q^2-9a^2+6a-1
更新1:
請寫埋step 越詳細越好
F.3 factorization
2006-10-22 12:46 am
1.(x+y)^4-(x-y)^4
2.(x-2y)^2-9a-54ay-81y^2
3.4x^2-36z^2-28xy+49y^2
4.p^2+6pq+9q^2-9a^2+6a-1
2.(x-2y)^2-9a-54ay-81y^2
3.4x^2-36z^2-28xy+49y^2
4.p^2+6pq+9q^2-9a^2+6a-1
回答 (2)
2006-10-22 1:37 am
✔ 最佳答案
1)(x+y)^4-(x-y)^4
= [(x+y)^2-(x-y)^2][(x+y)^2+(x-y)^2]
= [(x+y)-(x-y)][(x+y)+(x-y)](x2^+2xy+y^2+x^2-2xy+y^2)
= (2y)(2x)(2x^2+2y^2)
= 8xy(x^2+y^2)
2)
(x-2y)^2-9a^2-54ay-81y^2
= (x-2y)^2-(9a^2+54ay+81y^2)
= (x-2y)^2-(3a+9y)^2
= [(x-2y)-(3a+9y)][(x-2y)+(3a+9y)]
= (x-11y-3a)(x+7y+3a)
3)
4x^2-36z^2-28xy+49y^2
= 4x^2-28xy+49y^2-36z^2
= (2x-7y)^2-(6z)^2
= (2x-7y-6z)(2x-7y+6z)
4)
p^2+6pq+9q^2-9a^2+6a-1
= (p+3q)^2-(3a-1)^2
= [(p+3q)+(3a-1)][(p+3q)-(3a-1)]
= (p+3q+3a-1)(p+3q-3a+1)
2006-10-22 4:01 am
1:(x+y)^4-(x-y)^4
= [(x+y)^2-(x-y)^2][(x+y)^2+(x-y)^2]
= [(x+y)-(x-y)][(x+y)+(x-y)](x^2+2xy+y^2+x^2-2xy+y^2)
= (x+y-x+y)(x+y+x-y)(x^2+x^2+2xy-2xy+y^2+y^2)
= (2y)(2x)(2x^2+2y^2)
= 8xy(x^2+y^2)
2:(x-2y)^2-9a^2-54ay-81y^2
= (x-2y)^2-(9a^2+54ay+81y^2)
= (x-2y)^2-(3a+9y)^2
= [(x-2y)-(3a+9y)][(x-2y)+(3a+9y)]
= (x-2y-3a-9y)(x-2y+3a+9y)
= (x-2y-9y-3a)(x-2y+9y+3a)
= (x-11y-3a)(x+7y+3a)
3:4x^2-36z^2-28xy+49y^2
= 4x^2-28xy+49y^2-36z^2
= (2x-7y)^2-(6z)^2
= [(2x-7y)+(6z)][(2x-7y)-(6z)]
= (2x-7y-6z)(2x-7y+6z)
4:p^2+6pq+9q^2-9a^2+6a-1
= (p+3q)^2-(3a-1)^2
= [(p+3q)+(3a-1)][(p+3q)-(3a-1)]
= (p+3q+3a-1)(p+3q-3a+1)
= [(x+y)^2-(x-y)^2][(x+y)^2+(x-y)^2]
= [(x+y)-(x-y)][(x+y)+(x-y)](x^2+2xy+y^2+x^2-2xy+y^2)
= (x+y-x+y)(x+y+x-y)(x^2+x^2+2xy-2xy+y^2+y^2)
= (2y)(2x)(2x^2+2y^2)
= 8xy(x^2+y^2)
2:(x-2y)^2-9a^2-54ay-81y^2
= (x-2y)^2-(9a^2+54ay+81y^2)
= (x-2y)^2-(3a+9y)^2
= [(x-2y)-(3a+9y)][(x-2y)+(3a+9y)]
= (x-2y-3a-9y)(x-2y+3a+9y)
= (x-2y-9y-3a)(x-2y+9y+3a)
= (x-11y-3a)(x+7y+3a)
3:4x^2-36z^2-28xy+49y^2
= 4x^2-28xy+49y^2-36z^2
= (2x-7y)^2-(6z)^2
= [(2x-7y)+(6z)][(2x-7y)-(6z)]
= (2x-7y-6z)(2x-7y+6z)
4:p^2+6pq+9q^2-9a^2+6a-1
= (p+3q)^2-(3a-1)^2
= [(p+3q)+(3a-1)][(p+3q)-(3a-1)]
= (p+3q+3a-1)(p+3q-3a+1)
參考: myself
收錄日期: 2021-04-25 00:00:18
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061021000051KK03568