Question

Пожалуйста номер 31.21.Заранее спасибо！

Answer 1

task/27253572
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31.21.
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1)
(a - y)(a+y)(a²+y²) =(a²-y²)(a²+y²) =(a²)² - (y²)² =a⁴  - b⁴ .
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2)
(7x+1)(7x-1)(49x²+1) =((7x)² -1²)(49x²+1) =(49x²-1)(49x²+1) =
(49x²)²-1² =49²x⁴ -1 = 2401x⁴ -1.        * * *  7⁴x⁴ -1  или  (7x)⁴ -1 * * *
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3)
(x -6y³)²(x+6y³)² = ((x -6y³)(x+6y³))² =(x² - 36y⁶)² .
* * * или   иначе x⁴-72x²y⁶ +1296y¹²  * * *
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4)
(8+x³)(8-x³)(64+x⁶) =( (8² -(x³)² )(64+x⁶) =(64-x⁶)(64+x⁶) =64²-(x⁶)²=
=64² - x¹² = 4096 - x¹² .                * * * или   иначе 8⁴ -(x³)⁴ * * *
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5)
(25x²+y²)(5x+y)(5x -y) =(25x²+y²)((5x)²-y²)=(25x²+y²)(25x²-y²) =(25x²)² -(y²)²=
625x⁴ -y⁴.         * * *   или   иначе(5x)⁴ - y⁴ * * *
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6)
(81a⁴ +16b⁴)(9b² +4a²)(4a²-9b²) =(81a⁴ +16b⁴)(4a²+9b²)(4a²-9b²) =
(81a⁴ +16b⁴)(4a²+9b²)(4a²-9b²) =(81a⁴ +16b⁴)((4a²)²-(9b²)² )=
(81a⁴ +16b⁴)(16a⁴ -81b⁴)  ??
------- наверно ------- 
(81b⁴ +16a⁴)(9b² +4a²)(4a²-9b²) =(16a⁴ +81b⁴)(4a²+9b²)(4a²-9b²) =
(16a⁴ +81b⁴)(4a²+9b²)(4a²-9b²) =(16a⁴ +81b⁴))((4a²)²-(9b²)² )=
(16a⁴ +81b⁴)(16a⁴ -81b⁴) =(16a⁴)² - (81b⁴)² =256a⁸ - 6561b⁸.
* * *  или   иначе (2a)⁸ -(3b)⁸ * * *