How would you solve this problem? Any help is appreciated.

Question

Can you find the pattern and write a general rule for the following two polynomials.

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

x^3 + 8 = (x + 2)(x^2 - 2x + 4)

Answer 1

The first equation is the difference of two cubes (cubes of 3x and 5)

The second equation is the sum of two cubes (cubes of x and 2)

General formulas

sum of cubes a^3 + b^3 = (a+b)(a^2-ab+b^2)

difference of cubes = a^3 - b^3 = (a-b)(a^2+ab+b^2)