Question

Вычислите наиболее рациональным способом: $137^{2} - 54 *137+27^{2}$
$\frac{82^{2} -18^{2} }{67^{2}-33^{2} }$

Answer 1

$1)137^{2}-54*137+27^{2}=137^{2}-2*27*137+27^{2}=(137-27)^{2}=\\\\=110^{2}=\boxed{12100} \\\\\\2)\frac{82^{2}-18^{2}}{67^{2}-33^{2}}=\frac{(82-18)(82+18)}{(67-33)(67+33)}=\frac{64*100}{34*100}=\frac{32}{17} =\boxed{1\frac{15}{17}}$