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ivanovatatj2
@ivanovatatj2
December 2021
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Пожалуйста решите 3 , 6
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Задание 3.
а) 16a² - 9 = (4a - 3)(4a + 3)
б) 3x³ - 75x = 3x (x² - 25) = 3x (x - 5)(x + 5)
в) 2x² + 4xy + 2y² = 2 (x² + 2xy + y²) = 2 (x + y)²
Задание 6.
а) 36a⁴ - 25a²b² = (6a²)² - (5ab)² = (6a² - 5ab)(6a² + 5ab) = a (6a - 5b) * a (6a + 5b) = a² (6a - 5b)(6a + 5b)
б) 9x² - (x - 1)² = (3x)² - (x - 1)² = (3x - (x - 1))(3x + (x - 1) = (3x - x + 1)(3x + x - 1) = (2x + 1)(4x - 1)
в) x³ + y⁶ = x³ + (y²)³ = (x + y²)(x² - xy² + y⁴)
Использованные формулы:
a² - b² = (a - b)(a + b)
a³ + b³ = (a + b)(a² - ab + b²)
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Answers & Comments
а) 16a² - 9 = (4a - 3)(4a + 3)
б) 3x³ - 75x = 3x (x² - 25) = 3x (x - 5)(x + 5)
в) 2x² + 4xy + 2y² = 2 (x² + 2xy + y²) = 2 (x + y)²
Задание 6.
а) 36a⁴ - 25a²b² = (6a²)² - (5ab)² = (6a² - 5ab)(6a² + 5ab) = a (6a - 5b) * a (6a + 5b) = a² (6a - 5b)(6a + 5b)
б) 9x² - (x - 1)² = (3x)² - (x - 1)² = (3x - (x - 1))(3x + (x - 1) = (3x - x + 1)(3x + x - 1) = (2x + 1)(4x - 1)
в) x³ + y⁶ = x³ + (y²)³ = (x + y²)(x² - xy² + y⁴)
Использованные формулы:
a² - b² = (a - b)(a + b)
a³ + b³ = (a + b)(a² - ab + b²)