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selena030201
@selena030201
July 2022
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разложите на множители: 1)(а-2в)⁴-8(а-2в)
2)(а-2в)³-(а+2в)³
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oppression
1)
(а-2b)⁴-8(а-2b)=((a-2b)³-8)(a-2b)=(a³-6a²b+12ab²-(2b)³-8)(a-2b)=(a³-6a²b+12ab²-8b³-8)(a-2b).
2)(а-2b)³-(а+2b)³=((a-2b)-(a+2b))((a-2b)²+(a-2b)(a+2b)+(a+2b)²)=(a-2b-a-2b)(a²-4ab+4b²+a²-4b²+a²+4ab+4b²)=(-4b)(3a²+4b²)=-4b(3a²+4b²).
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Answers & Comments
2)(а-2b)³-(а+2b)³=((a-2b)-(a+2b))((a-2b)²+(a-2b)(a+2b)+(a+2b)²)=(a-2b-a-2b)(a²-4ab+4b²+a²-4b²+a²+4ab+4b²)=(-4b)(3a²+4b²)=-4b(3a²+4b²).