Factor the Polynomial completely:

10x^4y-20x^2y^2

10x2y(x2 -2y)

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To factor the polynomial 10x^4y - 20x^2y^2 completely, we can start by factoring out the greatest common factor (GCF) from each term.

The GCF of 10x^4y and -20x^2y^2 is 10x^2y. By factoring out the GCF, we have:

10x^2y( x^2 - 2y )

Now, let's focus on the expression within the parentheses, x^2 - 2y. This expression cannot be factored further since it has no common factors or perfect square terms. Therefore, the factored form of the polynomial 10x^4y - 20x^2y^2 is:

10x^2y( x^2 - 2y )