Question

How to factor 9x^4-6x^2y^4+y^89x4−6x2y4+y8

Answer 1

Answer:

$(3x^2-y^4)(3x^2-y^4)$

Step-by-step explanation:

We'll assume the correct expression to be factored is

$9x^4-6x^2y^4+y^8$

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

$\sqrt{9x^4}=3x^2$

$\sqrt{y^8}=y^4$

Since both are exact, we'll test if the middle term is twice the product of both square roots:

$2(3x^2)(y^4)=6x^2y^4$

We confirm the middle term equals the above expression. All tests confirm the original expression is

$\left ( 3x^2-y^4 \right )^2$

The required factoring is

$(3x^2-y^4)(3x^2-y^4)$