How do you simplify #9x^2-5x^4#?

1 Answer
Alan P.
Sep 28, 2015

#9x^2-5x^4 = x^2(3-sqrt(5)x)(3+sqrt(5)x)#

Explanation:

#9x^2-5x^2#

#color(white)("XXX")#extracting the obvious factor of #x^2#
#=x^2(9-5x^2)#

#color(white)("XXX")#remember that #(a^2-b^2) = (a-b)(a+b)#
#color(white)("XXX")#and substituting #9 = 3^2# for #a^2#
#color(white)("XXX")#and #5x^2 = (sqrt(5)x)^2# for #b^2#
#=x^2(3-sqrt(5)x)(3+sqrt(5)x)#

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