Question

решите плз (c+3)^3-(c-3)^3

Answer 1

1 способ

Применим формулу: a³-b³ = (a-b)(a²+ab+b²)

 (c+3)³ - (c-3)³ =

= (c+3-(c-3))((c+3)²+(c+3)(c-3)+(c-3)²) =

= (c+3-c+3)(c²+6c+9+c²-9+c²-6c+9) =

= 6·(3c²+9) = 18c²+ 54

2 способ

Применим формулы:

(a+b)³ = a³+3a²b+3ab²+b³;

(a-b)³ = a³-3a²b+3ab²-b³;

 (c+3)³ - (c-3)³ =

= (c³+3·c²·3+3·c·3²+3³) - (c³-3·c²·3+3·c·3²-3³) =

= (c³+9c²+27c+27) - (c³-9c²+27c-27) =

= c³+9c²+27c+27 - c³+9c²-27c+27 = 18c²+ 54

Ответ:  18c²+ 54