Question

Докажите тождество.
(c ^ 2 + 4c + 4)(c ^ 3 - 6c ^ 2 + 12c - 8) * (c + 2) = (c ^ 2 - 4) ^ 3

Answer 1

a² - b² = (a - b)(a + b)
(a + b)² = a² + 2ab + b²
(a - b)³ = a³ - 3a²b + 3ab² - b³
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(c² + 4c + 4)(c³ - 6c² + 12c - 8)(c + 2) = (c + 2)²(c - 2)³(c + 2) = (c + 2)³(c -2)³ = ((c - 2)(c + 2))³ = (c² - 4)³ чтд