How to simplify ${(x^{2} + 1)}^{2} + 2 (x^{2} + 1) + 1$ $(x^2+1)^2+2(x^2+1)+1$ ?

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Answer 1 · 2017-02-01T17:44:46

See below.

$y^{2} + 2 y + 1 = {(y + 1)}^{2}$ $y^2+2y+1=(y+1)^2$ so

${(x^{2} + 1)}^{2} + 2 (x^{2} + 1) + 1 = {(x^{2} + 2)}^{2}$ $(x^2+1)^2 + 2(x^2+1) +1=(x^2+2)^2$

Answer 2 · 2017-02-01T17:47:11

${(x^{2} + 2)}^{2}$ $(x^2+2)^2$ .

Let $f (x) = {(x^{2} + 1)}^{2} + 2 (x^{2} + 1) + 1, and, (x^{2} + 1) = y$ $f(x)=(x^2+1)^2+2(x^2+1)+1, and, (x^2+1)=y$

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

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

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