Question

Fatore os binômios:
a) 8a³+1
b) x³+64
c) 27a³+8y³

Answer 1

a) $8a^3 + 1 = (2a+1)*(4a^2-2a+1)$

b) $x^3+64 = (x+4)*(x^2-4x+16)$

c) $27a^3+8y^3 = (2y+3a)*(4y^2-6ay+9a^2)$

Answer 2

(a+b)³=a³+3a²b+3ab²+b³
(a+b)³=a³+b³+3ab(a+b)
a³+b³=(a+b)*[(a+b)²-3ab]
a³+b³=(a+b)*(a²+b²-ab]  

a) 8a³+1 =(2a)³+1 = (2a+1)*(4a²+1-2a)


b) x³+64 =x³+4³=(x+4)*(x²+16-4x)


c) 27a³+8y³ =(3a)³+(2y)³=(3a+2y)*(9a²+4y²-6ay)