化简求值[﹙a+1/2b)^2-(a-1/2b)^2](2a-1/2b)(1/2b+2a)(1/4b^2+4a^2)(其中a=-1,b=2)

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化简求值[﹙a+1/2b)^2-(a-1/2b)^2](2a-1/2b)(1/2b+2a)(1/4b^2+4a^2)(其中a=-1,b=2)

化简求值[﹙a+1/2b)^2-(a-1/2b)^2](2a-1/2b)(1/2b+2a)(1/4b^2+4a^2)(其中a=-1,b=2)
化简求值[﹙a+1/2b)^2-(a-1/2b)^2](2a-1/2b)(1/2b+2a)(1/4b^2+4a^2)(其中a=-1,b=2)

化简求值[﹙a+1/2b)^2-(a-1/2b)^2](2a-1/2b)(1/2b+2a)(1/4b^2+4a^2)(其中a=-1,b=2)
原式
= [(a+1/2b+a-1/2b)(a+1/2b-a+1/2b)]²(4a²-1/4b²)(4a²+1/4b²)
= [2ab]²(16a^4-1/16b^4)
= 64a^6b² - 1/4a²b^6
= 64×(-1)^6×2² - 1/4×(-1)²×2^6
= 256 - 16
= 240
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