Sure, let's solve the given algebraic expression step-by-step.
We are given the expression [tex]\((x + y)^2 - 4x^2y^2\)[/tex].
1. Expansion of [tex]\((x + y)^2\)[/tex]:
Start by expanding the square of the binomial.
[tex]\[
(x + y)^2 = x^2 + 2xy + y^2
\][/tex]
2. Substitute the expanded form:
Now substitute this expanded form back into the given expression.
[tex]\[
(x + y)^2 - 4x^2y^2 = x^2 + 2xy + y^2 - 4x^2y^2
\][/tex]
3. Simplify the expression:
Combine like terms, if any. Here, we just need to write down all terms clearly:
[tex]\[
x^2 + 2xy + y^2 - 4x^2y^2
\][/tex]
So the expanded form of [tex]\((x + y)^2 - 4x^2y^2\)[/tex] is:
[tex]\[
-4x^2y^2 + x^2 + 2xy + y^2
\][/tex]
This is the simplified form of the given algebraic expression.
