1. $[\mathbf{3}]$ What is the sum of all of the distinct prime factors of $25^{3}-27^{2}$ ?
Answer: 28 We note that $25^{3}-27^{2}=5^{6}-3^{6}=\left(5^{3}-3^{3}\right)\left(5^{3}+3^{3}\right)=(5-3)\left(5^{2}+5 \cdot 3+3^{2}\right)(5+$ 3) $\left(5^{2}-5 \cdot 3+3^{2}\right)=2 \cdot 7^{2} \cdot 2^{3} \cdot 19$, so the sum of the distinct prime factors is $2+7+19=28$.