簡易多項式的因式分解(f.2)

1. 169(x-y)^2-234(x-y)+81
設(x-y)為A,
(13A)^2 - 234A + 9^2
= (13A-9)^2
∵A = (x-y)
= [13(x-y)-9]^2

2. (a-b)^2+14(a-b)+49
設(a-b)為B,
B^2 + 14B +7^2
= (B+7)^2
∵B = (a-b)
= (a-b+7)^2

3. 3(m+2n)^2-14(m+2n)(m-n)-5(m- n)^2
設(m+2n)為X, (m- n)為Y
3X^2 - 14XY - 5Y^2
= (3X + Y )(X - 5Y)
∵X = (m+2n), Y = (m- n)
= [3(m+2n) + (m- n) ][ (m+2n) - 5(m- n)]
= (3m + 6n + m - n)(m + 2n - 5m + 5n)
= (4m +5n)(7n - 4m)

1. 169(x-y)^2-234(x-y)+81
=(13(x-y)^2-2(13(x-y))(9)+9^2)
=(13(x-y)-9)^2
2. (a-b)^2+14(a-b)+49
=(a-b)^2+2(7)(a-b)+7^2
=(a-b+7)^2
3. 3(m+2n)^2-14(m+2n)(m-n)-5(m-n)^2
=(4m +5n)(7n - 4m)

1. [13(x-y)-9]^2
=(13x-13y-9)^2
2 (a-b+7)^2
3. [3(m+2n)+(m-n)][m+2n-5(m-n)]
=(4m+5n)(7n-4m)

2007-08-27 13:34:50 補充：
No steps.Only by cross multiplicationjust treat x-y as a new termlike Let a=x-yc=a-b....by (a十/-b)^２=a^2十/-2ab b^2