54x^3 +250 factor

sum of two cubes:

(a^3+b^3)=(a+b)(a^2-ab+b^2)

cubrt (54x^3)=3xcubrt2
cubrt (250)=5cubrt2
Let k=cubrt2

(3xk+5k)(9x^2k^2-15xk^2+25*k^2)

k^3 (3x+5)(9x^2-15x+25) and k^3=2

I'd have factored out the 2 first, leaving

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

To factor the expression 54x^3 + 250, we can first look for any common factors that can be factored out. In this case, both terms have a common factor of 2.

Step 1: Factoring out the common factor:
2(27x^3 + 125)

Now, let's focus on the expression inside the parentheses, 27x^3 + 125. This is a sum of cubes, which can be factored using the following formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Step 2: Applying the sum of cubes formula:
2(3x + 5)(9x^2 - 15x + 25)

Therefore, the fully factored form of 54x^3 + 250 is 2(3x + 5)(9x^2 - 15x + 25).