How do you factor #-50x^2 + x^4 + 49#?

1 Answer
George C.
Dec 28, 2015

Factor as a quadratic in #x^2#, then use the difference of squares identity twice to find:

#-50x^2+x^4+49 = (x-7)(x+7)(x-1)(x+1)#

Explanation:

#-50x^2+x^4+49#

#= (x^2)^2-50(x^2)+49#

#= (x^2)^2-(49+1)(x^2)+(49xx1)#

#= (x^2-49)(x^2-1)#

#= (x^2-7^2)(x^2-1^2)#

#= (x-7)(x+7)(x-1)(x+1)#

using the difference of squares identity:

#a^2-b^2 = (a-b)(a+b)#

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