Question

x⁴+x²+1
give me step by step explanation

Answer 1

$\begin{gathered}\Large{\bold{\blue{\underline{Formula \: Used \::}}}} \end{gathered}$

$(1). \: \boxed{ \red{\tt \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}}$

$(2). \: \boxed{ \green{\tt \: (x + y)(x - y) = {x}^{2} - {y}^{2}}}$

$\large\underline\purple{\bold{Solution :- }}$

$\bf :\implies\: {x}^{4} + {x}^{2} + 1$

$\longmapsto \red{ \tt \: Adding \: and \: subtracting \: {x}^{2} }$

$\rm :\implies\: {x}^{4} + {x}^{2} + 1 + {x}^{2} - {x}^{2}$

$\rm :\implies\: {x}^{4} + {2x}^{2} + 1 - {x}^{2}$

$\rm :\implies\: {( {x}^{2} + 1) }^{2} - {x}^{2}$

$\bf :\implies\:( {x}^{2} + 1 - x)( {x}^{2} + 1 + x)$