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How to factor ##4x^4+81##?
##(2x^2-6x+9)(2x^2+6x+9)##
This is how to solve without using a specific theorem:
##4x^4+81##
Add ##36x^2## to complete the square and subtract ##36x^2## to equal to zero
##4x^4+36x^2+81-36x^2## ##(2x^2+9)^2-36x^2##
Answer: ##(2x^2-6x+9)(2x^2+6x+9)##