利用平方差的恆等式，因式分解下列各多項式。

1.36a^2-25b^2
=(6a+5b)(6a-5b)

2.(a+b)^2-c^2
=(a+b+c)(a+b-c)

3.3x^3-27x
=3x(x^2-9)
=3x(x+3)(x-3)

4.4x(y+z)^2-36x
=4x[(y+z)^2-9]
=(y+z+3)(y+z-3)

5.p^2-q^2-4pr-4qr
=(p+q)(p-q)-4(p+q)
=(p+q)(p-q-4)

6.4m^2-n^2+6m+3n
=(2m+n)(2m-n)+3(2m+n)
=(2m+n)(2m-n+3)

2010-02-19 21:58:48 補充：
4.4x(y+z)^2-36x
=4x[(y+z)^2-9]
=4x(y+z+3)(y+z-3)

2010-02-19 22:14:09 補充：
Thank you tonyleung052 for reminding me.
5.p^2-q^2-4pr-4qr
=(p+q)(p-q)-4r(p+q)
=(p+q)(p-q-4r)

36a^2-25b^2
(6a-5b)(6a+5b)

(a+b)^2-c^2
(a+b-c)(a+b+c)

3x^3-27x
3x(x^2-9)
3x(x+3)(x-3)

4x(y+z)^2-36x
4x((y+z)^2-9)
4x(y+z-3)(y+z+3)

p^2-q^2-4pr-4qr
(p^2-q^2)-4r(p+q)
(p+q)(p-q)-4r(p+q)
(p+q)(p-q-4r)

4m^2-n^2+6m+3n
(4m^2-n^2)+3(2m+n)
(2m+n)(2m-n)+3(2m+n)
(2m+n)(2m-n+3)

001wingkei :

You made mistake in Q5