Answer:
(6 - 9x^3)(36 + 54x^3 + 81x^6)
Step-by-step explanation:
To factor the expression 216 - 729x^9 as a sum or difference of perfect cubes, we first need to express each term as a cube.
First, let's rewrite 216 and 729x^9 as cubes:
216 = 6^3
729x^9 = (9x^3)^3
Now, we can use the formula for the difference of cubes:
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Substituting our values:
216 - 729x^9 = (6^3 - (9x^3)^3)(6^2 + 6(9x^3) + (9x^3)^2)
= (6 - 9x^3)(36 + 54x^3 + 81x^6)
So, (216 - 729x^9) can be factored as (6 - 9x^3)(36 + 54x^3 + 81x^6)
