Is this the correct answer?

Question

Divide 125y³ + 8x³ by 2x + 5y

(A) ∅

(B) 4x² + 25y²

(C) (2x+5y)²

(D) 4x² - 10xy + 25y²

(E) None of the above

For this I got; (B) 4x² - 10xy + 25y². Is this the correct answer?

Answer 1

8x^3 + 125y^3

———————

   2x + 5y

Notice that:

8x^3 = (2x)^3 

     and 

125y^3 = (5y)^3.  

So, the expression can be re-written with the numerator is the sum of 2 cubes:

(2x)^3 + (5y)^3

———————

    2x + 5y

The sum of 2 cubes can be factored as follows:

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

So, we can further rewrite the expression: 

(2x + 5y) ( (2x)^2 - (2x)(5y) + (5y)^2 )

———————————————————

        (2x + 5y)

The “2x + 5y” in the numerator and denominator cancel, and you’re left with

(2x)^2 - (2x)(5y) + (5y)^2, which simplifies to:

4x^2 - 10xy + 25y^2, answer D.