F.2 Maths Identies and Factoriziation

1)
4x^2 - y^2 / 12x^2 - 4xy - y^2

=[ (2x)^2 - y^2 ] / (6x+y) (2x-y)

呢度用十字相乘法 ( 註三 )

=(2x+y) (2x-y) / (6x+y) (2x-y)

=(2x+y) / (6x+y)


2)
6-11a+4a^2 / 14-a-3a^2

=4a^2-11a+6 / -(3a^2+a-14)

=(4a-3) (a-2) / -(3a+7) (a-2)

兩處都係用左十字相乘法 ( 註二 & 三 )

=(4a-3) / -(3a+7)


註一:
12x^2 - 4xy - y^2
6x y
2x -y
-6xy+2xy=-4xy
=(6x+y)(2x-y)

註二:
4a^2-11a+6
4a -3
a -2
-8a-3a=-11a
= (4a-3)(a-2)

註三:
(3a^2+a-14)
3a 7
a -2
7a-6a=a
=(3a+7)(a-2)

4x^2-y^2 / 12x^2-4xy-y^2
=-(2x-y)(2x+y)/[y+6x)(y-2x)]
=(2x+y)/(y_6x)


6-11a+4a^2 / 14-a-3a^2
=-(4a-3)(a-2)/[(3a+7)(a-2)]
=-(4a-3)/(3a+7)