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дракон100
@дракон100
August 2022
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Представьте многочлен в виде произведения:
3a^3 - 3b^3 + 5a^2 - 5b^2
a^4 - a^3b + ab^3- b^4
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nafanya2014
Verified answer
3a³ - 3b³ + 5a²- 5b²=3(a³-b³)+5(a²-b²)=3(a-b)(a²+ab+b²)+5(a-b)(a+b)=(a-b)(3a²+3ab+5b²+5a+5b)
a⁴ - a³b + ab³- b⁴=(a⁴-b⁴)-(a³b-ab³)=(a²-b²)(a²+b²)-ab(a-b)=(a-b)(a+b)(a²+b²)-ab(a-b)=
=(a-b)( (a+b)(a²+b²)-ab)=(a-b)(a³+a²b+ab²+b³-ab)
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Verified answer
3a³ - 3b³ + 5a²- 5b²=3(a³-b³)+5(a²-b²)=3(a-b)(a²+ab+b²)+5(a-b)(a+b)=(a-b)(3a²+3ab+5b²+5a+5b)a⁴ - a³b + ab³- b⁴=(a⁴-b⁴)-(a³b-ab³)=(a²-b²)(a²+b²)-ab(a-b)=(a-b)(a+b)(a²+b²)-ab(a-b)=
=(a-b)( (a+b)(a²+b²)-ab)=(a-b)(a³+a²b+ab²+b³-ab)