How to factor $a^2(a+1/a)^2-4a^2(a+1/a)+4a^2$ to get $(a-1)^4$?

Question

I get $a^2(a+1/a-2)^2$, do you keep going from here or did I do it completely incorrectly?

Answer 1

You are on the right track. Now notice just that $$a^2(a+1/a-2)^2 = (a(a+1/a-2))^2 = (a^2-2a+1)^2.$$

Answer 2

you are right

$$a^2\left(a+\frac{1}{a}-2\right)^2=a^2\left(\frac{a^2-2a+1}{a}\right)^2=a^2\frac{(a-1)^4}{a^2}=(a-1)^4$$

Answer 3

$$a^2(a+\frac{1}{a}-2)^2$$ $$(a(a+\frac{1}{a}-2))^2$$ $$(a^2-2a+1)^2$$ $$((a-1)^2)^2$$

$$(a-1)^4$$