Question

Решите пожалуйста. А то я чётко не понимаю.

Answer 1

$\displaystyle a). \ \ \ a^{4}-2a^{3}+a^{2}-1 = a^{2}(a^{2}-2a+1)-1=a^{2}(a-1)^{2}-1=\\\\=(a(a-1))^{2}-1=(a(a-1)-1)(a(a-1)+1)=\\\\=(a^{2}-a-1)(a^{2}-a+1);\\\\\\b). \ \ \ b^{4}-b^{2}-2b-1=b^{4}-(b^{2}+2b+1)=b^{4}-(b+1)^{2}=\\\\=(b^{2}-b-1)(b^{2}+b+1);$

$\displaystyle c). \ \ \ c^{8}-c^{4}-2c^{2}-1=(c^{4})^{2}-((c^{2})^{2}+2c^{2}+1)=\\\\=(c^{4})^{2}-(c^{2}+1)^{2}=(c^{4}-c^{2}-1)(c^{4}+c^{2}+1)=\\\\=(c^{4}-c^{2}-1)(c^{4}+2c^{2}+1-c^{2})=\\\\=(c^{4}-c^{2}-1)((c^{2}+1)^{2}-c^{2})=\\\\=(c^{4}-c^{2}-1)(c^{2}+1-c)(c^{2}+1+c);$