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Question
What should be taken away from 3x2 - 4y2 + 5xy + 20 to obtain - x2 - y2 + 6xy + 20?
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Solution
Let p be the required term.
(3x2 - 4y2 + 5xy + 20) - p = - x2 - y2 + 6xy + 20
p = (3x2 - 4y2 + 5xy + 20) - (- x2 - y2 + 6xy + 20)
= 3x2 - 4y2 + 5xy + 20 + x2 + y2 - 6xy - 20
= 3x2 + x2 - 4y2 + y2 + 5xy - 6xy + 20 - 20
= 4x2 - 3y2 - xy
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