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4\left(b^{2}x^{2}+2b^{2}\right)
Factor out 4.
b^{2}\left(x^{2}+2\right)
Consider b^{2}x^{2}+2b^{2}. Factor out b^{2}.
4b^{2}\left(x^{2}+2\right)
Rewrite the complete factored expression. Polynomial x^{2}+2 is not factored since it does not have any rational roots.