Mathematics
x4 - y4 + x2 - y2 is equal to:
(x + y + 1) (x + y - 1) (x2 + y2)
(x + y) (x - y) (x2 + y2 - 1)
(x + y) (x - y) (x2 + y2 + 1)
none of these
Factorisation
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Answer
x4 - y4 + x2 - y2
Using the formula
[∵ (x2 - y2) = (x + y)(x - y)]
= (x4 - y4) + (x2 - y2)
= (x2 - y2)(x2 + y2) + (x - y)(x + y)
= (x - y)(x + y)(x2 + y2) + (x - y)(x + y)
= (x - y)(x + y)((x2 + y2) + 1)
= (x - y)(x + y)(x2 + y2 + 1)
Hence, option 3 is the correct option.
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