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Solve by multiplying the first two polynomials first.

This gets you $3a^3-2a^2-12a+6a^2-4a-24$ which simplifies down to $3a^3+4a^2-16a-24$

Now you do $(a^2-2a+1)(3a^3+4a^2-16a+24)$

After multiplying, you get $3a^5+4a^4-16a^3-24a^2-6a^4-8a^3+32a^2+48a+3a^3+4a^2-16a-24$

$3a^5+4a^4-16a^3-24a^2-6a^4-8a^3+32a^2+48a+3a^3+4a^2-16a-24$ simplifies down to $3a^5-2a^4-21a^3+12a^2+32a-24$

So the answer is $3a^5-2a^4-21a^3+12a^2+32a-24$