f.4 maths

81x^2y - 54xy^2 +36y^3=9y(9x^2 - 6xy +4y^2)
108x^3 + 32y^3=4(27x^3 + 8y^3)=4(3x+2y)(9x^2 - 6xy + 4y^2)
H.C.F=9x^2 - 6xy +4y^2
L.C.M=36y(3x+2y)(9x^2 - 6xy +4y^2)

16a^2 +40ab +25b^2= (4a+5b)^2
16a^3- 4a^2b -30ab^2=2a(8a^2- 2ab -15b^2)=2a(4a+5b)(2a-3b)
H.C.F=4a+5b
L.C.M=2a(2a-3b)(4a+5b)^2


2010-04-28 20:23:54 補充：
The common factor of the three terms 81x^2y, - 54xy^2 and 36y^3 is 9y.
Threrfore 81x^2y - 54xy^2 +36y^3=9y(9x^2 - 6xy +4y^2)
81x^2y=9y(9x^2)
- 54xy^2=9y(- 6xy)
36y^3=9y(4y^2)

2010-04-28 20:24:57 補充：
This is only an explaination.
For calculation, my orginal step is okay.

2010-04-28 21:28:05 補充：
That's okay.
If you still don't understand them, you can ask me.