因式分解：（1）3分之1a^2-3b^2（2）-4x^2-9y^2-30xy(5)(x+y)^3-(x-y)^3

Question

因式分解：（1）3分之1a^2-3b^2 （2）-4x^2-9y^2-30xy (5)(x+y)^3-(x-y)^3

Answer 1

3分之1a^2-3b^2
=1/3(a^2-9b^2)
=1/3(a+3b)(a-3b)
-4x^2-9y^2-30xy
=-(4x^2+9y^2+30xy)
=进行不下去了
(x+y)^3-(x-y)^3
=[x+y-(x-y)][(x+y)^2+(x+y)(x-y)+(x-y)^2]
=2y*(2x^2+2y^2+x^2-y^2)
=2y*(3x^2+y^2)