southernbrowninggirl
southernbrowninggirl southernbrowninggirl
  • 02-12-2018
  • Mathematics
contestada

which of the following expression is equal to -3x^2-12?
a. (-3x+6i)(x+2i)
b. (-3x-6i)(x+2i)
c. (-3x+2i)(x-6i)
d. (-3x-4i)(x-3i)

99 POINTS!!!!! HELP

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gmany
gmany gmany
  • 02-12-2018

[tex]i=\sqrt{-1}\to i^2=-1\\\\-3x^2-12=-3(x^2+4)=-3(x^2+2^2)=-3(x^2-(-2^2))\\\\=-3(x^2-(-1\cdot2^2))=-3(x^2-(i^2\cdot2^2))=-3(x^2-(2i)^2)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=-3(x-2i)(x+2i)\\\\\text{use distributive property}\\\\=\boxed{(-3x+6i)(x+2i)}\to\boxed{a.}[/tex]

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