Show that `(x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot`

Explanation

To prove that \((x^2 + y^2)^4 = (x^4 - 6x^2y^2 + y^4)^2 + (4x^3y - 4xy^3)^2\), we will start with the left-hand side (LHS) and manipulate it to match the right-hand side (RHS).

### Step-by-step Solution:

1. **Start with LHS**:
\[ \text{LHS} = (x^2 + y^2)^4 \]
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