Question

Разложите на множители: 1) - 2) - 256

Answer 1

$1)a ^{8} -b ^{8} =(a ^{4} ) ^{2} -(b ^{4} ) ^{2} =(a ^{4} -b ^{4} )(a ^{4} +b ^{4} )= \\ =(a ^{2} -b ^{2} )(a ^{2} +b ^{2} )(a ^{4} +b ^{4} )=(a-b)(a+b)(a ^{2} +b ^{2} )(a ^{4} +b ^{4} )$

$2)a ^{16} -256=(a ^{8} ) ^{2} -16 ^{2} =(a ^{8} -16)(a ^{8} +16) =\\ =((a ^{4} ) ^{2} -4 ^{2} )(a ^{8} +16)=(a ^{4} -4)(a ^{4} +4)(a ^{8} +16)= \\ =(a ^{2} -2)(a ^{2} +2)(a ^{4} +4)(a ^{8} +16)= \\ =(a- \sqrt{2} )(a+ \sqrt{2} )(a ^{2} +2)(a ^{4} +4)(a ^{8} +16)$