Choose one of the factors of 500x^3 + 108y^18

Answers: 25x^2 + 15xy^6 + 9y^2
All of the above
6
5x + 3y^6

Question

Choose one of the factors of 500x^3 + 108y^18

Answers:    25x^2 + 15xy^6 + 9y^2 
                  All of the above 
                  6 
                 5x + 3y^6

aroub · Answer

5x + 3y^6

aroub · Answer

anonymous · Answer

supposed to recognize this as "difference of two cubes"
$$a^3-b^2=(a-b)(a^2+ab+b^2)$$

anonymous · Answer

or rather "sum of two cubes"
$$(a^3+b^3=(a+b)(a^2-ab+b^2)$$

anonymous · Answer

first factor out a 4 to get 
$$4(125x^3+27y^{18})$$ and now 
$$a=5x,b=3y^6$$ use the formula get 
$$4(5x+3y^6)(25x^2-15xy^6+9y^{12})$$

anonymous · Answer

so it looks like answer 1 is possible but it is wrong because of the sign