Determine if the polynomial (x^4 - 2x^2y^2 + y^4) is a perfect square. If so, factor it.

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Accepted Answer

Step:1 ：First, recognize that the given polynomial has the form (a^2 - 2ab + b^2), which is the square of a binomial.Step:2 ：In this case, (a = x^2) and (b = y^2). Therefore, the polynomial can be written as ((x^2 - y^2)^2).Step:3 ：To confirm this, expand ((x^2 - y^2)^2) to get (x^4 - 2x^2y^2 + y^4), which matches the original polynomial.

Answer

Step: 1 ：First, recognize that the given polynomial has the form (a^2 - 2ab + b^2), which is the square of a binomial.Step: 2 ：In this case, (a = x^2) and (b = y^2). Therefore, the polynomial can be written as ((x^2 - y^2)^2).Step: 3 ：To confirm this, expand ((x^2 - y^2)^2) to get (x^4 - 2x^2y^2 + y^4), which matches the original polynomial.

Determine if the polynomial \(x^4 - 2x^2y^2 + y^4\) is a perfect square. If so, factor it.

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