Question

(1-x^2)(1-y^2)+4xy
Factorise it

Answer 1

$(1-x^{2})(1-y^{2}) + 4xy \\= 1(1-y^{2}) - x^{2}(1-y^{2})\\= 1 - y^{2} - x^{2} + x^{2}y^{2} + 4xy \\=( 1 + x^{2}y^{2} + 2xy ) - ( x^{2} + y^{2} - 2xy )\\= [ 1^{2} + (xy)^{2} + 2\times 1\times xy ] - ( x - y )^{2} \\= ( 1 + xy )^{2} - ( x - y )^{2} \\= [ 1 + xy + ( x - y )][ 1 + xy - ( x - y) ] \\= ( 1 + xy + x - y )( 1 + xy - x + y )$

Therefore.,

$\red {(1-x^{2})(1-y^{2}) + 4xy}$

$\green { = ( 1 + xy + x - y )( 1 + xy - x + y )}$

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