Mathematics
Factorise the following:
9 - x2 + 2xy - y2.
Factorisation
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Answer
9 - x2 + 2xy - y2
Above terms can be written as,
9 - x2 + xy + xy - y2.
or,
9 - x2 + xy + 3x - 3x + 3y - 3y + xy - y2
Rearranging above terms, we get,
9 - 3x + 3y + 3x - x2 + xy + xy - 3y - y2.
Take out common in all terms we get,
3(3 - x + y) + x(3 - x + y) + y(-3 - y + x)
= 3(3 - x + y) + x(3 - x + y) - y(3 - x + y)
= (3 + x - y)(3 - x + y).
Hence, 9 - x2 + 2xy - y2 = (3 + x - y)(3 - x + y).
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