Используем формулы:
a³ + b³ = (a+b)(a²-ab+b²)
a³ - b³ = (a-b)(a²+ab+b²)
1)
(b-5)³+125 =
= (b-5)³+5³ =
= (b-5+5)((b-5)²-(b-5)·5+5²) =
= b·(b²-10b+25-5b+25+25)=
= b·(b²-15b+75)
2)
(4-3x)³-8x³ =
= (4-3x)³ - (2x)³ =
= (4-3x-2x)((4-3x)² +(4-3x)·2x+(2x)²) =
= (4-5x)·(16-24x+9x²+8x-6x²+4x²)=
= (4-5x)·(16-16x+7x²) =
= (4-5x)·(7x²-16x+16)
3)
(a-b)³+(a+b)³ =
= (a-b+a+b)((a-b)²-(a-b)(a+b)+(a+b)²) =
= 2a·(a²-2ab+b²-a²+b²+a²+2ab+b²) =
= 2a·(a²+3b²)
Используем формулы:
(a+b)³ = a³ + 3a²b+ 3ab² + b³
(a-b)³ = a³ - 3a²b+ 3ab² - b³
4)
(c+3)³-(c-3)³ =
= (c³ + 3·3c²+ 3·c·3² + 3³) - (c³ - 3·3c²+ 3·c·3² - 3³) =
= (c³ + 9c²+ 27c + 27) - (c³ - 9c²+ 27c - 27) =
= c³ + 9c²+ 27c + 27 - c³ + 9c²- 27c + 27 =
= 18c² + 54 = 18·(c²+3)