數學因式分解...

27a^2 - 12b^2
=3(9a^2-4b^2)
=3(3a+2b)(3a-2b)






50a^2 - 18b^2c^2
=2(25a^2-9b^2c^2)
=2(5a-3bc)(5a+3bc)






4a^3 - (b^2 - 6b + 9)a
=a(4a^2-(b^2-6b+9))
=a(4a^2-(b-3)^2)
=a(2a-b+3)(2a+b-3)









1 - x^2 + 4xy - 4y^2
=1-(x^2-4xy+4y^2)
=1-(x-2y)^2
=(1-x+2y)(1+x-2y)

2010-01-24 14:22:03 補充：
第一條:抽個3,再用恆等式(a-b)(a+b),finish!

第二條:抽個2,再用恆等式(a-b)(a+b),finish!

第三條:抽個a,make(b^2 - 6b + 9)to(b-3)^2,用恆等式(a^2+2ab+b^2),再用恆等式(a-b)(a+b),
finish!!

第四條,把 - x^2 + 4xy - 4y^2 change to -(x^2-4xy+4y^2),再change to-(x-2y)^2!!

2010-01-24 14:24:11 補充：
唔好以為1-(x-2y)^2好多野,當-(x-2y)^2一個term,甘就好easy!!

27a^2 - 12b^2
=3(9a^2-4b^2)
=3(3a+2b)(3a-2b)

50a^2 - 18b^2c^2
=2(25a^2-9b^2c^2)
=2(5a-3bc)(5a+3bc)

4a^3 - (b^2 - 6b + 9)a
=a(4a^2-(b^2-6b+9))
=a(4a^2-(b-3)^2)
=a(2a-b+3)(2a+b-3)

1 - x^2 + 4xy - 4y^2
=1-(x^2-4xy+4y^2)
=1-(x-2y)^2
=(1-x+2y)(1+x-2y)

27a^2 - 12b^2

= 3(9a^2 - 4b^2)

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

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

50a^2 - 18b^2c^2

= 2(25a^2 - 9b^2c^2)

= 2((5a)^2 - (3bc)^2)

= 2(5a+3bc)(5a-3bc)

4a^3 - (b^2 - 6b + 9)a

= a (4a^2 - (b^2 - 6b + 9))

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

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

1 - x^2 + 4xy - 4y^2

= 1^2 - (x^2 - 4xy + 4y^2)

= 1^2 - (x - 2y)^2

= (1 + x - 2y)(1 - x + 2y)