Factor completely.
\[
80 x^{4}-5 y^{4}
\]
Final Answer: The factored form of the expression \(80 x^{4}-5 y^{4}\) is \(\boxed{5*(2*x - y)*(2*x + y)*(4*x^2 + y^2)}\)
Step 1 :Given the expression \(80 x^{4}-5 y^{4}\)
Step 2 :Recognize that this is a difference of two squares, which can be factored using the formula \(a^2 - b^2 = (a+b)(a-b)\)
Step 3 :In this case, \(a\) is \(\sqrt{80x^4}\) and \(b\) is \(\sqrt{5y^4}\)
Step 4 :Factorize the given expression using the difference of squares formula
Step 5 :The factored form of the expression is \(5*(2*x - y)*(2*x + y)*(4*x^2 + y^2)\)
Step 6 :Final Answer: The factored form of the expression \(80 x^{4}-5 y^{4}\) is \(\boxed{5*(2*x - y)*(2*x + y)*(4*x^2 + y^2)}\)