幾題數學唔識…因式分解

yatyat

2008-11-17 2:11 am

因式分解下列題目。
m(x+y)^2-4m(x-y)^2

4a^2(y-2)^2-a^2

9a^2-4b^2-9a-6b

請寫埋步驟，我想學識點計…

回答 (1)

Uncle Michael

2008-11-17 2:44 am

✔ 最佳答案

Let a = x+y

and b = x-y

m(x+y)2 - 4m(x-y)2

= m[(x+y)2 - 4(x-y)2]

= m(a2 - 4b2)

= m[a2 - (2b)2]

= m[a + 2b][a - 2b]

= m[(x+y) + 2(x-y)][(x+y)-2(x-y)]

= m[x + y + 2x - 2y][x + y - 2x + 2y]

= m(3x - y)(-x + 3y)

= m(3x - y)(3y - x)

=====
Let b = y - 2

4a2(y-2)2 - a2

= 4a2b2 - a2

= a2(4b2 - 1)

= a2[(2b)2 - 12]

= a2[2b + 1][2b - 1]

= a2[2(y - 2) + 1][2(y - 2) - 1]

= a2[2y - 4 + 1][2y - 4 - 1]

= a2(2y - 3)(2y - 5)

=====
9a2 - 4b2 - 9a - 6b

= [9a2 - 4b2] - [9a + 6b]

= [(3a)2 - (2b)2] - [9a + 6b]

= (3a + 2b)(3a - 2b) - (3a + 2b)3

= (3a + 2b)[(3a - 2b) - 3]

= (3a + 2b)(3a - 2b - 3)
=

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