Expand the expression using the Binomial Theorem.
\[
(2 p+1)^{4}
\]
$(2 p+1)^{4}=\square($ Simplify your answer.)
Final Answer: The expanded form of the expression \((2 p+1)^{4}\) is \(\boxed{16 p^{4} + 32 p^{3} + 24 p^{2} + 8 p + 1}\).
Step 1 :Given the expression \((2 p+1)^{4}\), we are asked to expand it using the Binomial Theorem.
Step 2 :The Binomial Theorem states that for any numbers a and b, and any natural number n, the expression \((a + b)^n\) can be expanded as the sum of the terms in the form of nCr * a^(n-r) * b^r, where nCr is the binomial coefficient.
Step 3 :In this case, a = 2p, b = 1, and n = 4. So, we can use the Binomial Theorem to expand the given expression.
Step 4 :Applying the Binomial Theorem, we get the expanded expression as \(16 p^{4} + 32 p^{3} + 24 p^{2} + 8 p + 1\).
Step 5 :Final Answer: The expanded form of the expression \((2 p+1)^{4}\) is \(\boxed{16 p^{4} + 32 p^{3} + 24 p^{2} + 8 p + 1}\).