How to factor 27u^3-125 completly?

27u^3-125
= (3u – 5)(9u² + 15u + 25)
a³ – b³ =(a – b)(a² + ab + b²)
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a^3 - b^3 ≡ (a - b)(a^2 + ab + b^2)

27u^3 - 125
= (3u)^3 - 5^3
= (3u - 5)(9u^2 + 15u + 25)

=(3u-5)(9u^2+15u+25)

To start, notice that 27 = 3*3*3 and 125 = 5*5*5 so we have the difference of two cubes, since each term 27u³ and 125 is a cube.

Using the general formula (a³-b³) = (a-b)(a²+ab+b²), we can substitute a = 3u and b = 5 to obtain

(3u-5)(9u²+15u+25) as our factors