Certainly! Let's break down the given expression step-by-step to expand and simplify it:
Given the expression:
[tex]$(a - b)^2 + 4a^2b^2$[/tex]
### Step 1: Expand [tex]\((a - b)^2\)[/tex]
First, we'll expand the squared term [tex]\((a - b)^2\)[/tex].
[tex]\[
(a - b)^2 = a^2 - 2ab + b^2
\][/tex]
### Step 2: Combine the expanded term with [tex]\(4a^2b^2\)[/tex]
Now we need to add the expansion we just found to the second term in the expression, [tex]\(4a^2b^2\)[/tex].
The expression now looks like this:
[tex]\[
a^2 - 2ab + b^2 + 4a^2b^2
\][/tex]
### Step 3: Combine like terms
There are no like terms to combine between [tex]\(a^2\)[/tex], [tex]\(-2ab\)[/tex], [tex]\(b^2\)[/tex], and [tex]\(4a^2b^2\)[/tex]. Therefore, the expanded and simplified form of the expression is:
[tex]\[
4a^2b^2 + a^2 - 2ab + b^2
\][/tex]
So, the fully expanded expression for [tex]\((a - b)^2 + 4 a^2 b^2\)[/tex] is:
[tex]\[
4a^2b^2 + a^2 - 2ab + b^2
\][/tex]
