數學難題 20分 !!

[匿名]

2009-12-24 10:57 pm

Factorize the following polynomails:
1-14k*k+49k*k*k*k

1-18k*k+49k*k*k*k-144y*y

60(x+2y)*60(x+2y)-38(x+2y)(x-y)-10(x-y)*(x-y)

(x+y)*(x+y)*(x+y)+(x-y)*(x-y)*(x-y)

a*a*a-b*b*b+3ab*b-3a*ab

x*x*x+y*y*y-(x+y)*(x+y)*(x+y)

(要詳細列式、我 F.2 程度. )
我唔識打square 和 cube , 唯有用*代替。
答得愈多愈好,唔識答某題就咪做那題啦!
Thank you! :)
(* 即係乘))

回答 (1)

用戶9724

2009-12-24 11:24 pm

✔ 最佳答案

Factorize the following polynomails:
1)1-14k*k+49k*k*k*k
=1-14k^2+49k^4
=(1-7k^2)^2
2)1-18k*k+49k*k*k*k-144y*y
=1-18k^2+49k^4-144y^2
=(1-7k^2)^2-(12y)^2
=(1-7k^2+12y)(1-7k^2-12y)
3)60(x+2y)(x+2y)-38(x+2y)(x-y)-10(x-y)*(x-y). ..題目打錯
=2[30(x+2y)^2-19(x+2y)(x-y)-5(x-y)^2]
=2[6(x+2y)-5(x-y)][5(x+2y)+(x-y)]
=2(6x+12y-5x+5y)(5x+10y+x-y)
=2(x+17y)(6x+9y)
=6(x+17y)(2x+3y)

4)(x+y)*(x+y)*(x+y)+(x-y)*(x-y)*(x-y)
=(x+y)^3+(x-y)^3
=[(x+y)+(x-y)][(x+y)^2-(x+y)(x-y)+(x-y)^2]
=2x[x^2+2xy+y^2-x^2+y^2+x^2-2xy+y^2]
=2x(x^2+3y^2)
5)a*a*a-b*b*b+3ab*b-3a*ab
=a^3-b^3+3ab^2-3a^2b
=(a-b)(a^2+ab+b^2)-3ab(a-b)
=(a-b)(a^2+ab+b^2-3ab)
=(a-b)(a^2-2ab+b^2)
=(a-b)(a-b)^2=(a-b)^3
6)x*x*x+y*y*y-(x+y)*(x+y)*(x+y)
=x^3+y^3-(x+y)^3
=(x+y)(x^2-xy+y^2)-(x+y)^3
=(x+y)[x^2-xy+y^2-(x+y)^2]
=(x+y)(x^2-xy+y^2-x^2-2xy-y^2)
=(x+y)(-3xy)= -3xy(x+y)

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