Question

x^4 +x^2 + 1

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Answer 1

Step-by-step explanation:

${x}^{4} + {x}^{2} + 1$

$= {( {x}^{2}) }^{2} + 2 \times {x}^{2} \times 1 + ( {1)}^{2} - {x}^{2}$

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

Now,

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

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

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Answer 2

{x}^{4} + {x}^{2} + 1x

4

+x

2

+1

= {( {x}^{2}) }^{2} + 2 \times {x}^{2} \times 1 + ( {1)}^{2} - {x}^{2}=(x

2

)

2

+2×x

2

×1+(1)

2

−x

2

{ ({x}^{2} + 1)}^{2} - {x}^{2}(x

2

+1)

2

−x

2

Now,

( {x}^{2} + 1 + {x}^{2} )( {x}^{2} + 1 - {x}^{2} )(x

2

+1+x

2

)(x

2

+1−x

2

)

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

2

+1)