Question

factor ( x^4 + 20x^2 + 100 ) completely. all factors in your answer should have integer coefficients.

Explanation:

Step1: Recognize perfect square trinomial

Let $y = x^2$, rewrite the expression:
$y^2 + 20y + 100$

Step2: Factor the quadratic trinomial

Match $y^2+20y+100$ to $(a+b)^2=a^2+2ab+b^2$, where $a=y$, $b=10$:
$(y + 10)^2$

Step3: Substitute back $y=x^2$

Replace $y$ with $x^2$:
$(x^2 + 10)^2$

Answer:

$\boldsymbol{(x^2 + 10)^2}$