Question 67302
You should recognise this as the dference of two cubes:
{{{64^3c^6 - 27x^9 = (4ac^2)^3 - (3x^3)^3}}}
The difference of two cubes can be factored as follows:
{{{A^3 - B^3 = (A-B)(A^2+2AB+B^2)}}}
In this problem; {{{A = 4ac^2}}} and {{{B = 3x^3}}} Applying the factor.
{{{(4ac^2) - (3x^3) = (4ac^2 - 3x^3)((4ac^2)^2 + 2(4ac^2)(3x^3) + (3x^3)^2)}}} Simplifying:
{{{(4ac^2 - 3x^3)(16a^2c^4 + 24ac^2x^3 + 9x^6)}}}