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Question
What should be added to x2 + xy + y2 to obtain 2x2 + 3xy?
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Solution
Let a be the required term.
a + (x2 + y2 + xy) = 2x2 + 3xy
a = 2x2 + 3xy - (x2 + y2 + xy)
a = 2x2 + 3xy - x2 - y2 - xy
a = 2x2 - x2 - y2 + 3xy - xy
= x2 - y2 + 2xy
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