数学化简计算(x+1)(x-1)(x^2-x+1)(x^2+x+1)
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数学化简计算(x+1)(x-1)(x^2-x+1)(x^2+x+1)
数学化简计算
(x+1)(x-1)(x^2-x+1)(x^2+x+1)
数学化简计算(x+1)(x-1)(x^2-x+1)(x^2+x+1)
=[(x-1)(x^2+x+1)][(x+1)(x^2-x+1)]
=(x^3-1)(x^3+1)
=x^6-1
[(x^2+1)^2- x^](x^-1)
(x+1)(x-1)(x^2-x+1)(x^2+x+1)
=(x^3+1)(x^3-1)
=x^6-1
原式=(x^2-1)[(x^2+1)^2-x^2]
=(x^2-1)(x^4+x^2+1)
=(x^2)^3-1
=x^6-1
(x+1)(x-1)(x^2-x+1)(x^2+x+1)
=[(x-1)(x^2+x+1)][(x+1)(x^2-x+1)]
=(x^3-1)(x^3+1)
=x^6-1
(x+1)(x-1)(x^2-x+1)(x^2+x+1)
=[(x-1)(x^2+x+1)][(x+1)(x^2-x+1)]
=(x^3-1)(x^3+1)
=x^6-1
你没学过立方和与立方差公式吧?
原式=x^2-1)[(x^2+1)^2-x^2]
=(x^2-1)(x^4+x^2+1)
=(x^2)^3-1
=x^6-1
用的是 平方差公式来化简
(x+1)(x-1)=x^2-1
但是(x^2-x+1)(x^2+x+1)没法简单的化,所以需打乱算式顺序来化
即 ;原式= (x+1)(x^2-x+1)(x-1)(x^2+x+1)
=(x^3-x^2+x+x^2-x+1)(x^3+x^2+x-x^2-x-1)
=(x^3+1)(x^3-1)
...
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用的是 平方差公式来化简
(x+1)(x-1)=x^2-1
但是(x^2-x+1)(x^2+x+1)没法简单的化,所以需打乱算式顺序来化
即 ;原式= (x+1)(x^2-x+1)(x-1)(x^2+x+1)
=(x^3-x^2+x+x^2-x+1)(x^3+x^2+x-x^2-x-1)
=(x^3+1)(x^3-1)
=(x^3)^2-1
化简结果为:(x^3)^2-1
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