ab=8,a-2b=4.求(a^2-4b^2)(a^2b+2ab^2)

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ab=8,a-2b=4.求(a^2-4b^2)(a^2b+2ab^2)
ab=8,a-2b=4.求(a^2-4b^2)(a^2b+2ab^2)

ab=8,a-2b=4.求(a^2-4b^2)(a^2b+2ab^2)
(a^2-4b^2)(a^2b+2ab^2)
=(a+2b)(a-2b)[ab(a+2b)]
=(a+2b)^2(a-2b)ab
(a+2b)^2=(a-2b)^2+8ab=16+64=80
则a+2b=±4根号5
则原式=±4根号5*4*8=±128根号5

(a+2b)²
=a²+4b²+4ab
=a²+4b²-4ab+8ab
=(a-2b)²+8ab
=4²+64
=16+64
=80
(a²-4b²)(a²b+2ab²)
=(a+2b)(a-2b)ab(a+2b)
=...

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(a+2b)²
=a²+4b²+4ab
=a²+4b²-4ab+8ab
=(a-2b)²+8ab
=4²+64
=16+64
=80
(a²-4b²)(a²b+2ab²)
=(a+2b)(a-2b)ab(a+2b)
=ab(a-2b)(a+2b)²
=8x4x80²
=32x6400
=204800

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