Question

Вычислите 2^32 × 5^8 − (80^4 − 1) × (80^4 + 1)

Answer 1

$2^{32} * 5^{8}-(80^4-1)(80^4+1)=2^{32} * 5^{8}-(80^8-1)=\\ =2^{24}*(2^{8} * 5^{8})-(80^8-1)=2^{24}*10^{8}-(80^8-1)=\\ =(2^{3})^{8}*10^{8}-(80^8-1)=8^{8}*10^{8}-(80^8-1)=\\ =80^8-80^8+1=1.$