Answer:
[tex](3x^2-y^4)(3x^2-y^4)[/tex]
Step-by-step explanation:
We'll assume the correct expression to be factored is
[tex]9x^4-6x^2y^4+y^8[/tex]
One must try to find out if the expression is a perfect square. To test it, we'll take the square root of the first and the last term. If they are exact, we'll procceed with the next step
[tex]\sqrt{9x^4}=3x^2[/tex]
[tex]\sqrt{y^8}=y^4[/tex]
Since both are exact, we'll test if the middle term is twice the product of both square roots:
[tex]2(3x^2)(y^4)=6x^2y^4[/tex]
We confirm the middle term equals the above expression. All tests confirm the original expression is
[tex]\left ( 3x^2-y^4 \right )^2[/tex]
The required factoring is
[tex](3x^2-y^4)(3x^2-y^4)[/tex]
