Final answer to the problem
$f\left(x\right)=x^{4}-2x^2+1$
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Apply the formula: $\left(a+b\right)^2$$=a^2+2ab+b^2$, where $a=x^2$, $b=-1$ and $a+b=x^2-1$
$f\left(x\right)=x^{4}-2x^2+1$
Final answer to the problem
$f\left(x\right)=x^{4}-2x^2+1$
