Разложи на множетели (t6+u6)2−(t6−u6)2−t2u2. Created by X1337. algebra-ru

Разложи на множетели (t6+u6)2−(t6−u6)2−t2u2...

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T12+u12 +2t6u6 - t12+2t6u6-u12-t2u2 = 4t6u6-t2u2 = (2t3u3-tu)(2t3u3+tu)

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(t⁶ + u⁶)² - (t⁶ - u⁶)² - t²u² = (t⁶ + u⁶ + t⁶ - u⁶)(t⁶ + u⁶ - t⁶ + u⁶) - t²u² =
= 2t⁶ * 2u⁶ - t²u² = 4t⁶u⁶ - t²u² = t²u²(4t⁴u⁴ - 1)=t²u²(2t²u² - 1)(2t²u² + 1)

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