Answer :

Final answer:

To factor the polynomial completely, group terms with common factors and factor out those common factors. The completely factored form of the given polynomial is -1(x^2(y - x)(y + x)) + 9((y - x)(y + x)).

Explanation:

To factor the given polynomial -x2y2 + x4 + 9y2 - 9x2 completely, we can group terms with common factors and factor out those common factors.

First, let's factor out a common factor of -1 from the first two terms and a common factor of 9 from the last two terms:

-x2y2 + x4 + 9y2 - 9x2 = -1(x2y2 - x4) + 9(y2 - x2)

Next, let's factor out common factors from both terms:

-1(x2y2 - x4) + 9(y2 - x2) = -1(x2(y2 - x2)) + 9((y - x)(y + x))

Therefore, the completely factored form of the given polynomial is:

-1(x2(y - x)(y + x)) + 9((y - x)(y + x))

Final answer:

To factor the polynomial -x^2y^2 + x^4 + 9y^2 - 9x^2 completely, we first factor out the greatest common factor and then factor each term separately.

Explanation:

To factor the polynomial -x^2y^2 + x^4 + 9y^2 - 9x^2, we can look for common factors. After factoring out the greatest common factor, which is -1, we have:

-1(x^2y^2 - x^4 - 9y^2 + 9x^2)

Now we can factor each of the terms separately. Factoring x^2y^2 and 9y^2 gives:

-1(x^2y^2 + 9y^2 - x^4 - 9x^2)

Factoring x^2 out of the first two terms and -1x^2 out of the last two terms, we get:

-1(x^2(y^2 + 9) - x^2(x^2 + 9))

Simplifying further, we have:

-1(x^2(y^2 + 9) - x^2(x^2 + 9))

Now we can factor out (y^2 + 9) and (x^2 + 9), leaving us with:

-1(x^2 - 1)(y^2 + 9)

So, the polynomial is factored as -1(x^2 - 1)(y^2 + 9).