factor ( x^4 - 18x^2 + 81 ) completely. all factors in your answer should have integer coefficients.

Answer:

$(x - 3)^2(x + 3)^2$

Explanation:

Step1: Substitute $y = x^2$

$y^2 - 18y + 81$

Step2: Factor the quadratic

$y^2 - 18y + 81 = (y - 9)^2$

Step3: Replace $y$ with $x^2$

$(x^2 - 9)^2$

Step4: Factor difference of squares

$(x^2 - 9) = (x - 3)(x + 3)$, so $(x^2 - 9)^2 = (x - 3)^2(x + 3)^2$