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Question

What should be added to 6x2 - 3xy + 4y2 to get 2y2 + xy - 4x2?

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Solution

Let px be added to 6x2-3xy+4y2 to get 2y2+xy-4x2.i.e., 6x2-3xy+4y2+px=2y2+xy-4x2px=2y2+xy-4x2-6x2-3xy+4y2px=2y2+xy-4x2-6x2+3xy-4y2px=2y2-4y2+xy+3xy-4x2-6x2px=-2y2+4xy-10x2px=-10x2-2y2+4xy-10x2-2y2+4xy can be added to 6x2-3xy+4y2 to get 2y2+xy-4x2.

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