Question 818731
{{{125c^6-8d^6}}}
The greatest common factor (GCF) is 1 (which we rarely bother factoring out).<br>
Next we try other factoring methods. One of these other methods is to use factoring patterns. And one of these patterns is:
{{{a^3-b^3 = (a-b)(a^2+ab+b^2)}}}
This pattern can be used on our expression because {{{125c^6}}} is a perfect cube, {{{(5c^2)^3}}}, and {{{8d^6}}} is also a perfect cube, {{{(2d^2)^3}}}. Using this pattern we get:
{{{((5c^2)-(2d^2))((5c^2)^2+(5c^2)(2d^2)+(2d^2)^2)}}}
which simplifies to:
{{{(5c^2-2d^2)(25c^4+10c^2 * d^2+4d^4)}}}
Neither of these factors will factor further, no matter which method we try, so we are finished.