R = |(a^4 + 4a^2)^(3/2) / (a^4 - 2a^3 + a^2)| * |(2-a)^2 / 4|Now, simplify

Sure, let's simplify the given expression step by step.

Given expression is:

R = |(a^4 + 4a^2)^(3/2) / (a^4 - 2a^3 + a^2)| * |(2-a)^2 / 4|

First, let's simplify the first part of the expression:

|(a^4 + 4a^2)^(3/2) / (a^4 - 2a^3 + a^2)|

We can rewrite a^4 + 4a^2 as (a^2)^2 + 22a^2, which is a perfect square trinomial. So, it can be factored as (a^2 + 2)^2.

So, the expression becomes:

|((a^2 + 2)^2)^(3/2) / (a^4 - 2a^3 + a^2)|

The square root of (a^2 + 2)^2 is a^2 + 2. So, when we raise it to the power of 3/2, we get (a^2 + 2)^3.

So, the expression becomes:

|(a^2 + 2)^3 / (a^4 - 2a^3 + a^2)|

Now, let's simplify the second part of the expression:

|(2-a)^2 / 4|

We can rewrite (2-a)^2 as 4 - 4a + a^2.

So, the expression becomes:

|(4 - 4a + a^2) / 4|

Now, let's put both parts together:

R = |(a^2 + 2)^3 / (a^4 - 2a^3 + a^2)| * |(4 - 4a + a^2) / 4|

This is the simplified form of the given expression.