化简[(a+1/2b)^2+(a-1/2b)^2](2a^2-1/2b^2)
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化简[(a+1/2b)^2+(a-1/2b)^2](2a^2-1/2b^2)
因式分解
因式分解
![化简[(a+1/2b)^2+(a-1/2b)^2](2a^2-1/2b^2)](/uploads/image/z/505229-5-9.jpg?t=%E5%8C%96%E7%AE%80%5B%28a%2B1%2F2b%29%5E2%2B%28a-1%2F2b%29%5E2%5D%282a%5E2-1%2F2b%5E2%29)
[(a+1/2b)^2+(a-1/2b)^2](2a^2-1/2b^2)
=[a^2+ab+1/4b^2+a^2-ab+1/4b^2](2a^2-1/2b^2)
=(2a^2+1/2b^2)(2a^2-1/2b^2)
=4a^4-1/4b^4
=[a^2+ab+1/4b^2+a^2-ab+1/4b^2](2a^2-1/2b^2)
=(2a^2+1/2b^2)(2a^2-1/2b^2)
=4a^4-1/4b^4
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