Question 146254
{{{9a^6b^8c^6-4d^8}}} Start with the given expression


{{{(3a^3b^4c^3)^2-4d^8}}} Rewrite {{{9a^6b^8c^6}}} as {{{(3a^3b^4c^3)^2}}}


{{{(3a^3b^4c^3)^2-(2d^4)^2}}} Rewrite {{{4d^8}}} as {{{(2d^4)^2}}}



Now use the difference of squares. Remember, the difference of squares formula is {{{A^2-B^2=(A+B)(A-B)}}} where in this case {{{A=3}}} and {{{B=2}}}


{{{9a^6b^8c^6-4d^8=(3a^3b^4c^3+2d^4)(3a^3b^4c^3-2d^4)}}} Plug in {{{A=3a^3b^4c^3}}} and {{{B=2d^4}}}


So the expression


{{{9a^6b^8c^6-4d^8}}}


factors to


{{{(3a^3b^4c^3+2d^4)(3a^3b^4c^3-2d^4)}}}


Notice that if you foil the factored expression, you get the original expression. This verifies our answer.