计算:(a^2+ab^2+b^4)(a^2-ab^2+b^4)-[(a-b^2)(a+b^2)]^2+3a^2 b^2(1-b)(b+1)
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(a^2+ab^2+b^4)(a^2-ab^2+b^4)-[(a-b^2)(a+b^2)]^2+3a^2 b^2(1-b)(b+1)
=(a^2+b^4+ab^2)(a^2+b^4-ab^2)-(a^2-b^4)^2+3a^2 b^2(1-b^2)
=(a^2+b^4)^2-(ab^2)^2-(a^2-b^4)^2+3a^2 b^2(1-b^2)
=(a^2+b^4)^2-(a^2-b^4)^2-(ab^2)^2+3a^2 b^2(1-b^2)
=[(a^2+b^4)-(a^2-b^4)][(a^2+b^4)+(a^2-b^4)]-(ab^2)^2+3a^2 b^2(1-b^2)
=2b^4*2a^2-(ab^2)^2+3a^2 b^2(1-b^2)
=4a^2b^4-a^2b^4+3a^2b^2-3a^2b^2*b^2
=3a^2b^4+3a^2b^2-3a^2b^4
=3a^2b^4-3a^2b^4+3a^2b^2
=3a^2b^2
=(a^2+b^4+ab^2)(a^2+b^4-ab^2)-(a^2-b^4)^2+3a^2 b^2(1-b^2)
=(a^2+b^4)^2-(ab^2)^2-(a^2-b^4)^2+3a^2 b^2(1-b^2)
=(a^2+b^4)^2-(a^2-b^4)^2-(ab^2)^2+3a^2 b^2(1-b^2)
=[(a^2+b^4)-(a^2-b^4)][(a^2+b^4)+(a^2-b^4)]-(ab^2)^2+3a^2 b^2(1-b^2)
=2b^4*2a^2-(ab^2)^2+3a^2 b^2(1-b^2)
=4a^2b^4-a^2b^4+3a^2b^2-3a^2b^2*b^2
=3a^2b^4+3a^2b^2-3a^2b^4
=3a^2b^4-3a^2b^4+3a^2b^2
=3a^2b^2
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