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Nastya14545
@Nastya14545
July 2022
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Помогите пожалуйста решить ... № 7 (6). № 8 (2)(3). № 9 (2)(4)
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flsh
№ 7 (6)
(... - 5b²)³ = ... - 15a²b⁸ + ... - ...
Перед нами разложение по формуле куб разности: (x - y)³ = x³ - 3x²y + 3xy² - y³.
Получаем окончательно:
(ab³ - 5b²)³ = a³b⁹ - 15a²b⁸ + 75ab⁷ - 125b⁶
№ 8 (2)
(a - 2b)³ - (a + b)²(a - 8b) = 27ab²
(a - 2b)³ - (a² + 2ab +b²)(a - 8b) = 27ab²
a³ - 6a²b + 12ab² - 8b³ - a³ + 8a²b - 2a²b + 16ab² - ab² + 8b³ = 27ab²
№ 8 (3)
(5x + y)³ - y(5x - y)² - 25x(x + y)² = 100x³
(5x + y)³ - y(25x² - 10xy + y²) - 25x(x² + 2xy + y²) = 100x³
125x³ + 75x²y + 15xy² + y³ - 25x²y + 10xy² - y³ - 25x³ - 50x²y - 25xy² = 100x³
№ 9 (2)
(8x - 3)²x - (4x - 1)³ = 7
(64x² - 48x + 9)x - (64x³ - 48x² + 12x - 1) = 7
64x³ - 48x² + 9x - 64x³ + 48x² - 12x + 1 = 7
-3x = 6
x = -2
№ 9 (4)
(4y - 3)³ - y(8y - 9)² = 0
64y³ - 144y² +108y - 27 - 64y³ + 144y² - 81y = 0
27y - 27 = 0
y = 1
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Answers & Comments
(... - 5b²)³ = ... - 15a²b⁸ + ... - ...
Перед нами разложение по формуле куб разности: (x - y)³ = x³ - 3x²y + 3xy² - y³.
Получаем окончательно:
(ab³ - 5b²)³ = a³b⁹ - 15a²b⁸ + 75ab⁷ - 125b⁶
№ 8 (2)
(a - 2b)³ - (a + b)²(a - 8b) = 27ab²
(a - 2b)³ - (a² + 2ab +b²)(a - 8b) = 27ab²
a³ - 6a²b + 12ab² - 8b³ - a³ + 8a²b - 2a²b + 16ab² - ab² + 8b³ = 27ab²
№ 8 (3)
(5x + y)³ - y(5x - y)² - 25x(x + y)² = 100x³
(5x + y)³ - y(25x² - 10xy + y²) - 25x(x² + 2xy + y²) = 100x³
125x³ + 75x²y + 15xy² + y³ - 25x²y + 10xy² - y³ - 25x³ - 50x²y - 25xy² = 100x³
№ 9 (2)
(8x - 3)²x - (4x - 1)³ = 7
(64x² - 48x + 9)x - (64x³ - 48x² + 12x - 1) = 7
64x³ - 48x² + 9x - 64x³ + 48x² - 12x + 1 = 7
-3x = 6
x = -2
№ 9 (4)
(4y - 3)³ - y(8y - 9)² = 0
64y³ - 144y² +108y - 27 - 64y³ + 144y² - 81y = 0
27y - 27 = 0
y = 1