Answer:
A. (5x³y²z + 3)(25x^6 y^4 z^2 - 15x³y²z + 9)
Explanation:
Since 125x^9 y^6 z^3 and 27 are perfect cubes, we'll use the sum of cubes formula, a³ + b³ = (a + b)(a² - ab + b²) where a is the cube root of 125x^9 y^6 z^3 and b is the cube root of 27.
∛125x^9 y^6 z^3 = 5x³y²z and ∛27 = 3.
We have now done a + b, which is now (5x³y²z + 3). Now, we need to find what (5x³y²z)² is. The answer is 25x^6 y^4 z^2. Now, we need to multiply 5x³y²z and 3. Just multiply 3 by 5.
3x5 = 15. Now we have 15x³y²z.
Now, we need to multiply b by b. b = 3
3x3 = 9
If I forgot to mention it, a is 5x³y²z and b is 3.
(a + b) = (5x³y²z + 3).
a² = 25x^6 y^4 z^2.
ab = 15x³y²z.
b² = 9
(5x³y²z + 3)(a² - ab + b²) = (5x³y²z + 3)(25x^6 y^4 z^2 - 15x³y²z + 9).
The only answer that matches this is A, so A is the answer.