已知a-b=1,a²+b²=13,求(a³-2b³)-(a²b-2ab²)-(ab²-b³)的值.
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![已知a-b=1,a²+b²=13,求(a³-2b³)-(a²b-2ab²)-(ab²-b³)的值.](/uploads/image/z/8659205-53-5.jpg?t=%E5%B7%B2%E7%9F%A5a-b%3D1%2Ca%26%23178%3B%2Bb%26%23178%3B%3D13%2C%E6%B1%82%EF%BC%88a%26%23179%3B-2b%26%23179%3B%EF%BC%89-%EF%BC%88a%26%23178%3Bb-2ab%26%23178%3B%EF%BC%89-%EF%BC%88ab%26%23178%3B-b%26%23179%3B%EF%BC%89%E7%9A%84%E5%80%BC.)
已知a-b=1,a²+b²=13,求(a³-2b³)-(a²b-2ab²)-(ab²-b³)的值.
已知a-b=1,a²+b²=13,求(a³-2b³)-(a²b-2ab²)-(ab²-b³)的值.
已知a-b=1,a²+b²=13,求(a³-2b³)-(a²b-2ab²)-(ab²-b³)的值.
(a³-2b³)-(a²b-2ab²)-(ab²-b³)=a³-b³-a²b+ab²=a²(a-b)+b²(a-b)=(a²+b²)(a-b)=13
(a^3-2b^3)-(ab^2-2ab^2)-(ab^2-b^3)
=a^3-b^3-a^2b+ab^2
=(a-b)(a^2+ab+b^2)-ab(a-b)
=(a-b)(a^2+b^2) (1)
把a-b=1和a^2+b^2=13代人(1)得:=1*13=13
所以所求代数式的值是13