Solve: a^4+3 a^2+4 - Vidyadip

Question

Solve:
$ a^4+3 a^2+4 $

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Answer

$ a^4+3 a^2+4 $
$ =a^4+4 a^2-a^2+4 $
$ =\left(a^4+4 a^2+4\right)-a^2 $
$ =\left[\left(a^2\right)^2+2 \times a^2 \times 2+2^2\right]-a^2 $
$ =\left(a^2+2\right)^2-a^2 $
$ =\left[\left(a^2+2\right)-a\right]\left[\left(a^2+2\right)+a\right] $
$ =\left(a^2-a+2\right)\left(a^2+a+2\right) $

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