Question 167092
June is not correct!
How do we know?
One way to prove this is to multiply the two factors, using FOIL, to see if you arrive at the given polynomial.
{{{(c^3+d^4)(c^6-c^3*d^4+d^8) = c^9-c^6*d^4+c^3*d^8+c^6*d^4-c^3*d^8+d^12}}} Simplifying.
{{{c^9+d^12}}} and this is not the same as the given polynomial of {{{c^9-d^12}}}
Another way is to recognize the given polynomial as the difference of two cubes:
{{{c^9-d^12 = (c^3)^3 - (d^4)^3}}} and the difference of two cubes is factored thus:
{{{A^3-B^3 = (A-B)(A^2+AB+B^2)}}} where: {{{A = c^3}}} and {{{B = d^4}}}
{{{(c^3)^3 - (d^4)^3 = (c^3-d^4)(c^6+c^3*d^4+d^8)}}} and this is not what June got!