Question

срочно помогите пожалуйста​

Answer 1

$\displaystyle\bf\\1)\\\\\frac{97^{3} +83^{3} }{180} +97\cdot 83=\frac{(97+83)(97^{2}-97\cdot 83+83^{2} ) }{180} +97\cdot 83=\\\\\\=\frac{180\cdot(97^{2} -97\cdot 83+83^{2} )}{180} +97\cdot83=97^{2} -97\cdot 83+83^{2}+97\cdot 83=\\\\\\=97^{2} +83^{2} =16298\\\\\\2)\\\\\frac{71^{3} +49^{3} }{120} +71\cdot 49=\frac{(71+49)(71^{2}-71\cdot 49+49^{2} ) }{120} +71\cdot 49=\\\\\\=\frac{120\cdot(71^{2} -71\cdot 49+49^{2} )}{120} +71\cdot49=71^{2} -71\cdot 49+49^{2}+71\cdot 49=$

$\displaystyle\bf\\=71^{2} +49^{2} =7442\\\\\\3)\\\\\frac{67^{3} +52^{3} }{119} +67\cdot 52=\frac{(67+52)(67^{2}-67\cdot 52+52^{2} ) }{119} +67\cdot 52=\\\\\\=\frac{119\cdot(67^{2} -67\cdot 52+52^{2} )}{119} +67\cdot52=67^{2} -67\cdot 52+52^{2}+67\cdot 52=\\\\\\=67^{2} +52^{2} =7193$

$\displaystyle\bf\\4)\\\\\frac{87^{3} -37^{3} }{50} -87\cdot 37=\frac{(87-37)(87^{2}+87\cdot 37+37^{2} ) }{50} -87\cdot 37=\\\\\\=\frac{50\cdot(87^{2} +87\cdot 37+37^{2} )}{50} -87\cdot37=87^{2} +87\cdot 37+37^{2}-87\cdot 37=\\\\\\=87^{2} +37^{2} =8938$