Ответ:
1.
(a + 3)² + (a - 3)(a + 3) + 6a =
= a² + 6a + 9 + a² - 9 + 6a = 2a² + 12a
2.
а) (2 - 3n)² - 9n⁴ = (2 - 3n)² - (3n²)² = (2 - 3n - 3n²)(2 - 3n + 3n²)
б) (a - 5) ² + 2(5 - a) + 1 = (a - 5)² - 2(a - 5) + 1 = ((a - 5) - 1)² = (a - 6)²
в) x⁶ - x⁴ - x² + 1 = x⁴(x² - 1) - (x² - 1) = (x² - 1)(x⁴ - 1) = (x² - 1)(x² - 1)(x² + 1) =
= (x² - 1)²(x² + 1) = (x - 1)²(x + 1)²(x² + 1)
г)
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Verified answer
Ответ:
1.
(a + 3)² + (a - 3)(a + 3) + 6a =
= a² + 6a + 9 + a² - 9 + 6a = 2a² + 12a
2.
а) (2 - 3n)² - 9n⁴ = (2 - 3n)² - (3n²)² = (2 - 3n - 3n²)(2 - 3n + 3n²)
б) (a - 5) ² + 2(5 - a) + 1 = (a - 5)² - 2(a - 5) + 1 = ((a - 5) - 1)² = (a - 6)²
в) x⁶ - x⁴ - x² + 1 = x⁴(x² - 1) - (x² - 1) = (x² - 1)(x⁴ - 1) = (x² - 1)(x² - 1)(x² + 1) =
= (x² - 1)²(x² + 1) = (x - 1)²(x + 1)²(x² + 1)
г)