已知ab^2=6,求ab(a^2b^5-ab^3-b)的值

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已知ab^2=6,求ab(a^2b^5-ab^3-b)的值已知ab^2=6,求ab(a^2b^5-ab^3-b)的值已知ab^2=6,求ab(a^2b^5-ab^3-b)的值ab(a^2b^5-ab^

已知ab^2=6,求ab(a^2b^5-ab^3-b)的值
已知ab^2=6,求ab(a^2b^5-ab^3-b)的值

已知ab^2=6,求ab(a^2b^5-ab^3-b)的值
ab(a^2b^5-ab^3-b)
=a^3b^6-a^2b^4-ab^2
=(ab^2)^3-(ab^2)^2-ab^2
=6^3-6^2-6
=216-42
=174

∵ a b ² = 6
∴ a b (a ² b ^ 5 - a b ³ - b)
= a ³ b ^ 6 - a ² b ^ 4 - a b ²
= (a b ²)³ - (a b ²)² - a b ²
= 6 ³ - 6 ² - 6
= 216 - 36 - 6
= 216 - 42
= 174