Yuii
contestada

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Factor the expression completely over the complex numbers.

y4 + 12y2 + 36

PLEASE HELP ASAP CORRECT ANSWER ONLY PLEASE Factor the expression completely over the complex numbers y4 12y2 36 class=

Respuesta :

gmany

[tex]y^4+12y^2+36=(y^2)^2+2\cdot y^2\cdot6+6^2=(y^2+6)^2\\\\=(y^2+6)(y^2+6)=(y^2-(i\sqrt6)^2)(y^2-(i\sqrt6)^2)\\\\=(y-i\sqrt6)(y+i\sqrt6)(y-i\sqrt6)(y+i\sqrt6)\\\\=(y-i\sqrt6)^2(y+i\sqrt6)^2\\\\Used:\\\\(a+b)^2=a^2+2ab+b^2\\\\a^2-b^2=(a-b)(a+b)[/tex]

konrad509

[tex]y^4+12y^2+36=\\\\ (y^2+6)^2=\\\\ ((y+\sqrt{-6})(y-\sqrt{-6}))^2=\\\\ (y+i\sqrt6)^2(y-i\sqrt6)^2=\\\\ (y^2+2i\sqrt6 y-6)(y^2-2i\sqrt6 y-6)[/tex]