729x¹⁵ + 1000
This is a case of a sum of cubes.
729 is the cube of 9
1000 is the cube of 10
x¹⁵ is the cube of x⁵
A sum of perfect cubes can be factored into
(a + b) (a² - ab + b²)
(9x⁵+ 10) ((9x⁵)²-(9x⁵)(10) + 10²)
(9x⁵ + 10) (81x¹⁰ - 90x⁵ + 100) THIS IS THE FACTORIZATION
9x⁵ (81x¹⁰ - 90x⁵ + 100) + 10(81x¹⁰ - 90x⁵ + 100)
729x¹⁵ - 810x¹⁰ + 900x⁵ + 810x¹⁰ - 900x⁵ + 1000
729x¹⁵ - 810x¹⁰ + 810x¹⁰ + 900x⁵ - 900x⁵ + 1000
729x¹⁵ + 1000