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How do you factor $x^{4} + 2 x^{2} + 1$ $x^4+2x^2+1$ ?

1 Answer

Oct 1, 2015

$(x^{4} + 2 x^{2} + 1) = {(x^{2} + 1)}^{2}$ $(x^4+2x^2+1) = (x^2+1)^2$

Explanation:

Temporarily replace $x^{2}$ $x^2$ with $t$ $t$ to get
$XXX t^{2} + 2 t + 1$ $color(white)("XXX")t^2+2t+1$
which should be recognizable as ${(t + 1)}^{2}$ $(t+1)^2$

Then reverse the replacement
$XXX {(x^{2} + 1)}^{2}$ $color(white)("XXX")(x^2+1)^2$

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