先化简再求值:a+b=1/2,a-b=1/3,求a³+a²b-ab²-b³的值.
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先化简再求值:a+b=1/2,a-b=1/3,求a³+a²b-ab²-b³的值.
先化简再求值:a+b=1/2,a-b=1/3,求a³+a²b-ab²-b³的值.
先化简再求值:a+b=1/2,a-b=1/3,求a³+a²b-ab²-b³的值.
a³+a²b-ab²-b³
=a²(a+b)-b²(a+b)
=(a+b)(a²-b²)
=(a+b)²(a-b)
=1/4×1/3
=1/12
a³+a²b-ab²-b³
=a²(a+b)-b²(a+b)
=(a²-b²)(a+b)
=(a+b)²(a-b)
因为a+b=1/2,a-b=1/3,
上式=(1/2)²×1/3=1/12
a³+a²b-ab²-b³=a²﹙a+b﹚-b²﹙a+b﹚
=﹙a+b﹚²﹙a-b﹚
=¼×1/3
=1/12
a³+a²b-ab²-b³=a³-b³+ab(a-b)
=(a-b)(a²+ab+b²)+ab(a-b)
=(a-b)(a²+2ab+b²)
=(a-b)(a+b)²
=1/3×1/4=1/12