How to simplify #(x^2+1)^2+2(x^2+1)+1# ?

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Answer 1 · 2017-02-01T17:44:46

See below.

#y^2+2y+1=(y+1)^2# so

#(x^2+1)^2 + 2(x^2+1) +1=(x^2+2)^2#

Answer 2 · 2017-02-01T17:47:11

#(x^2+2)^2#.

Let #f(x)=(x^2+1)^2+2(x^2+1)+1, and, (x^2+1)=y#

#:. f(x)=y^2+2y+1=(y+1)^2#

#rArr f(x)={(x^2+1)+1}^2=(x^2+2)^2.#