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Mathematics

Factorise :

4x4 + 9y4 + 11x2y2

Factorisation

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Answer

Given,

    4x4 + 9y4 + 11x2y2

= (2x2)2 + (3y2)2 + 12x2y2 - x2y2

= (2x2)2 + (3y2)2 + 2 × 2x2 × 3y2 - x2y2

= (2x2 + 3y2)2 - (xy)2

= (2x2 + 3y2 + xy)(2x2 + 3y2 - xy).

Hence, 4x4 + 9y4 + 11x2y2 = (2x2 + 3y2 + xy)(2x2 + 3y2 - xy).

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