Question

Factorise 1+x^2y^2+x^2+y^2​

Answer 1

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

/* Rearranging the terms we get */

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

Therefore.,

$\red { Factors \:of \: 1 + x^{2}y^{2} + x^{2} + y^{2}}$

$\green {= (y^{2} + 1 )( 1 + x^{2} ) }$

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