1.

Factorise (1+x)²(1+y²)-(1-y)²(1+x²)

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Answer:

the answer is that it DEPENDS on the domain. in the INTEGERS, RATIONAL numbers and real numbers, the answer is no. However, in the COMPLEX numbers, where there is a solution to x^2+1=0, you can factor into (x-i)(x+i), where i^2=-1 (this number is no more imaginary than π).

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