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Pro100SuperKir
@Pro100SuperKir
August 2021
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Разложите многочлен на множители: (Решение+ответ)
1) a³+a²-a-1
2) a³+b³-a²b-ab²
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1)a^3+a^2-a-1=a^2(a+1)-(a+1)=(a+1)(a^2-1)=(a+1)(a+1)(a-1)
2)a^3+b^3-a^2b-ab^2=(a^3+b^3)-ab(a+b)=(a+b)(a^2-2ab+b^2)-ab(a+b)=(a+b)(a^2-ab+b^2-ab)=(a+b)(a^2-2ab+b^2)=(a+b)(a-b)^2
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Verified answer
1)a^3+a^2-a-1=a^2(a+1)-(a+1)=(a+1)(a^2-1)=(a+1)(a+1)(a-1)2)a^3+b^3-a^2b-ab^2=(a^3+b^3)-ab(a+b)=(a+b)(a^2-2ab+b^2)-ab(a+b)=(a+b)(a^2-ab+b^2-ab)=(a+b)(a^2-2ab+b^2)=(a+b)(a-b)^2