factor completely a^9+b^12 c^15

does not factor using rationals.

yes there's an a

= (a^3)^3 + (b^4c^5)^3

= (a^3 + b^4c^5)(x^6 - a^3b^4c^5 + b^8c^10)

To factor the expression a^9 + b^12 c^15, we can look for common factors among the terms. However, it seems that there are no common factors among the terms in this expression.

Therefore, the expression a^9 + b^12 c^15 cannot be factored any further. It is already in its simplest form.

Please let me know if there is anything else I can help you with.