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).
