Question

Factorise : x^4+x^2+25

Answer 1

In view of expressing the given expression as difference of perfect squares, split $x^2$ as $10x^2-9x^2$ :

$x^4+x^2+25~=~x^4+10x^2-9x^2+25\\=x^4+10x^2+25-9x^2\\=(x^2+5)^2-(3x)^2\\=(x^2+5+3x)(x^2+5-3x)\\=(x^2+3x+5)(x^2-3x+5)$

Answer 2

first you need to split the middle term.

=$x^{4} +10 x^{2} -9 x^{2} +25$

=$x^{4}+10 x^{2} +25-9 x^{2}$

=$( x^{2}+5 )^{2} - (3x)^{2}$     ($(a^{2} - b^{2} = (a+b)(a-b) )$

=$( x^{2} +5+3x) ( x^{2} +5-3x)$

The factors are : $( x^{2} +3x+5)( x^{2} -3x+5)$