Factor `500x^3 + 108` .
First, factor common factor of 4.
Now, notice that `125x^3` is perfect cube because `5^3` = 125 and `x^3` is a cube. Also 27 is a cube as `3^3` = 27
Now apply the rule of the sum of cubes.
`a^3 + b^3 = (a + b)(a^2-2ab+b^2)`
This problem indicates `a = 5x` and `b = 3`
Therefore, `4(5x+3)(25x^2 -30x+9)`
The factored solution to `500x^3+108` is `4(5x+3)(25x^2 -30x+9)`
Factor out the GCF of `4` from each term in the polynomial.
Factor out the GCF of `4` from `500x^3+108`
Since both terms are perfect cubes, the binomial can be factored using the sum of cubes formula: `a^3+b^3 = (a+b)(a^2-ab+b^2)`
The answer will be,