Question
Factorise $:x^4+ y^4- 3x^2y^2$
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Answer
$x^4+ y^4- 3x^2y^2$
$= x^4 + y^4 - 2x^2y^2 - x^2y^2$
$= (x^2)^2 + (y^2)^2 - 2x^2y^2 - x^2y^2$
$= ( x^2 - y^2 )^2 - (xy)^2$
$= ( x^2 - y^2 - xy )( x^2 - y^2 + xy ) [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= x^4 + y^4 - 2x^2y^2 - x^2y^2$
$= (x^2)^2 + (y^2)^2 - 2x^2y^2 - x^2y^2$
$= ( x^2 - y^2 )^2 - (xy)^2$
$= ( x^2 - y^2 - xy )( x^2 - y^2 + xy ) [ \because a^2 - b^2 = ( a + b )( a - b )]$
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