Question
Factorise $:4x^4+ 9y^4+ 11x^2y^2$
✓
Answer
$4x^4+ 9y^4+ 11x^2y^{2}$
$= (2x^2)^2 + (3y^2)^2 + 12x^2y^2 - x^2y^2$
$= (2x^2 + 3y^2)^2 - x^2y^2$
$= (2x^2 + 3y^2)^2 - (xy)^2$
$= ( 2x^2 + 3y^2 - xy )( 2x^2 + 3y^2 + xy)$
$ [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= (2x^2)^2 + (3y^2)^2 + 12x^2y^2 - x^2y^2$
$= (2x^2 + 3y^2)^2 - x^2y^2$
$= (2x^2 + 3y^2)^2 - (xy)^2$
$= ( 2x^2 + 3y^2 - xy )( 2x^2 + 3y^2 + xy)$
$ [ \because a^2 - b^2 = ( a + b )( a - b )]$
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