Автор - YchenickIzShkoly

разложите на множители
(3+q)^3+(3+5q)^3
(p-1)^3+(4+4p)^3

Ответ

Автор - nKrynka
(3+q)^3+(3+5q)^3 = (3 + q + 3 + 5q)*[(3 + q)² - (3 + q)*(3 + 5q) + (3 + 5q)²] = 
= 6*(1 + q)*(9 + 6q + q² - 9 - 18q - 5q² + 9 + 30q + 25q²) = 
= 18*(1 + q)*(7q² + 6q + 3)

(p-1)^3+(4+4p)^3 = (p - 1 + 4 + 4p)*[(p - 1)² - (p -1)*(4 + 4p) + (4 + 4p)²] =
= (5p + 3)*(p² - 2p + 1 - 4p² + 4 + 16 + 32p + 16p²) =
 = (5p + 3)*(13p² + 30p + 21)

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