Question

РАЗЛОЖИТЬ НА МНОЖИТЕЛЬ 1/27b^3+a^9, 25/169m^6-343/729n^3, (5b+4)^3-125, 16x^3+(3x+2)^3

Answer 1

1/27b³+a⁹=(1/3b)³+(a³)³=(1/3b+a³)((1/3b)²-a³/3b+(a³)²)=

(1/3b+a³)(1/9b²-a³/3b+a⁶)

25/169m⁶-343/729n³=(5/13)²(m²)³- (7³/9³n³)=(5/13)²(m²)³ - (7/9n)³

(5b+4)³-125=(5b+4)³-5³=(5b+4-5)((5b+4)²-(5b+4)*5+5²)=

=(5b-1)((5b+4)²-5(5b+4)+25)=(5b-1)(25b²+40b+16-25b-20+25)=

(5b-1)(25b²+15b+21)

6x³+(3x+2)³= 6x³+(3x)³+3(3x)²*2+3*3x*2²+2³=6x³+9x³+54x²+36x+8=

15x³+54x²+36x+8=