Question

Factorise 8x^3-1/27+125y^3+10xy

Answer 1

We in the polynomial that
a) first 3 terms are cubes of: 2x, -1/3 and 5y
b) fourth term is 3 time multiplication of a)

Using three variable cubic identity:
x^3 + y^3 + z^3 - 3xyz = (x+y+z) (x^2 + y^2 + z^2 - xy- xz - yz)

Given polynomial can be expressed as:
=> (2x)^3 + (-1/3)^3 + (5y)^3 + 3(2x)(-1/3)(5y)
= (2x - 1/3 + 5y) ((2x)^2 + (-1/3)^2 + (5y)^2 - (2x)(-1/3) - (-1/3)(5y) - (2x)(5y) )
= (2x - 1/3 + 5y) (4x^2 + 1/9 + 25y^2 + 2x/3 + 5y/3 - 10xy)