How do I factor, 4X^2 -4-X^2 Y^2 +Y^2?

Question

Since I can't make an exponent with my keyboard I used '^'. It would look like this in a calculator: 4(X^2)-4-(X^2)•(Y^2)+(Y^2). Where the parenthesis are being used to group the exponent to the variable, not to show multiplication. Sorry for explaining the obvious, I just want to make sure it is clear.

Answer 1

4X^2-4-X^2 Y^2+Y^2



Factor the greatest common factor (GCF) from each group.



(4(X^2-1)-Y^2 (X^2-1))



Factor the polynomial by grouping the first 2 terms together and finding the greatest common factor (GCF). Next group the second two terms together and find the GCF. Since both groups contain the factor (X^2-1), they can be combined.



(4-Y^2)(X^2-1)



The first group can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is X^2-b^2=(X-b)(X+b).



(2-Y)(2+Y)(X^2-1)



The same is true for the second group.



(2-Y)(2+Y)(X+1)(X-1)



QED

Answer 2

4(x^2-1)-y^2(x^2-1)=(x^2-1)(4-y^2)=(x-1)(x+1)(2-y)(2+y)

Answer 3

4X^2 -4-X^2 Y^2 +Y^2

x^2(4-Y^2)-(4-Y^2)

(4-Y^2)(x^2-1)