1. The problem is to divide the expression $16p^4 - 81q^4$ by $2p + 3q$ without using any special formulas. 2. We will use polynomial long division step-by-step, just like dividing numbers. 3. First, divide the first term of the dividend $16p^4$ by the first term of the divisor $2p$ to get $8p^3$. 4. Multiply the entire divisor $2p + 3q$ by $8p^3$ to get $16p^4 + 24p^3q$. 5. Subtract this from the original dividend: $$ (16p^4 - 81q^4) - (16p^4 + 24p^3q) = -24p^3q - 81q^4 $$ 6. Now divide the first term of the new expression $-24p^3q$ by $2p$ to get $-12p^2q$. 7. Multiply the divisor by $-12p^2q$: $$ -12p^2q(2p + 3q) = -24p^3q - 36p^2q^2 $$ 8. Subtract this from the previous remainder: $$ (-24p^3q - 81q^4) - (-24p^3q - 36p^2q^2) = 0 - 81q^4 + 36p^2q^2 = 36p^2q^2 - 81q^4 $$ 9. Divide the first term $36p^2q^2$ by $2p$ to get $18pq^2$. 10. Multiply the divisor by $18pq^2$: $$ 18pq^2(2p + 3q) = 36p^2q^2 + 54pq^3 $$ 11. Subtract this from the current remainder: $$ (36p^2q^2 - 81q^4) - (36p^2q^2 + 54pq^3) = 0 - 81q^4 - 54pq^3 = -54pq^3 - 81q^4 $$ 12. Divide the first term $-54pq^3$ by $2p$ to get $-27q^2$. 13. Multiply the divisor by $-27q^2$: $$ -27q^2(2p + 3q) = -54pq^3 - 81q^4 $$ 14. Subtract this from the remainder: $$ (-54pq^3 - 81q^4) - (-54pq^3 - 81q^4) = 0 $$ 15. The remainder is zero, so the division is exact. 16. The quotient is: $$ 8p^3 - 12p^2q + 18pq^2 - 27q^2 $$ This completes the division without using any special formulas.