Question

Разложите на множители 81-d¹²​

Answer 1

$81 - d {}^{12} = (9 - d {}^{6})(9 + d {}^{6} ) = \\ (3 - d {}^{3} )(3 + d^{3} )(9 + d {}^{6} )$

Answer 2

Ответ:

$\boxed{\ x^2-y^2=(x-y)(x+y)\ \ ,\ \ x^3\pm y^3=(x\pm y)(x^2\mp xy+y^2)\ \ }\\\\\\\\81-d^{12}=9^2-(d^6)^2=(9-d^6)(9+d^6)=(3^2-(d^3)^2)(9+d^6)=\\\\=(3-d^3)(3+d^3)(9+d^6)=\\\\=(\sqrt[3]3-d)(\sqrt[3]9+\sqrt[3]3d+d^2)(\sqrt[3]3+d)(\sqrt[3]9-\sqrt[3]3d+d^2)(9+d^6)$