分解因式m^2/9-(mn)/3+n^2/4-3ax^2+6axy-3ay^2(x^2+4)^2+8x(x^2+4)+16x^2

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分解因式m^2/9-(mn)/3+n^2/4-3ax^2+6axy-3ay^2(x^2+4)^2+8x(x^2+4)+16x^2

分解因式m^2/9-(mn)/3+n^2/4-3ax^2+6axy-3ay^2(x^2+4)^2+8x(x^2+4)+16x^2
分解因式m^2/9-(mn)/3+n^2/4
-3ax^2+6axy-3ay^2
(x^2+4)^2+8x(x^2+4)+16x^2

分解因式m^2/9-(mn)/3+n^2/4-3ax^2+6axy-3ay^2(x^2+4)^2+8x(x^2+4)+16x^2
m^2/9-(mn)/3+n^2/4
=(m/3)^2-2(m/3)(n/2)+(n/2)^2
=(m/3-n/2)^2;
-3ax^2+6axy-3ay^2
=-3a(x^2-2xy+y^2)
=-3a(x-y)^2;
(x^2+4)^2+8x(x^2+4)+16x^2
=(x^2+4)^2+2(4x)(x^2+4)+(4x)^2
=(x^2+4+4x)^2
=[(x+2)^2]^2
=(x+2)^4