Factor the polynomial completely. 8x^4y – 16x^2y^2

8\,x^2\,y\,(x-\sqrt{2} )(x+\sqrt{2} )

Step-by-step explanation:

Let's start by extracting all common factors from the two terms of this binomial. These common factors are: 8, , and .

The extraction renders:

In the real number system, the binomial in parenthesis can still be factored out considering that 2 is the perfect square of , that is:

We can then forwards with the factoring of this binomial using the factorization of a difference of squares as:

Thus giving the complete factorization as:

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step-by-step explanation: