Expand the expression using the Binomial Theorem:
$$(2x+1{)}^5=◻x^5+◻x^4+◻x^3+◻x^2+◻x+◻$$

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Step 1 ：Define a function to calculate the binomial coefficient. This function will take two arguments, n and k, and return the binomial coefficient of n choose k.

Step 2 ：Use this function to calculate the coefficients for each term in the expansion of the expression $(2x+1{)}^5$.

Step 3 ：Substitute a=2, b=1, and n=5 into the formula for each term to get the expanded expression.

Step 4 ：Calculate the binomial coefficient for each term in the expansion, multiply it by $a^{(n-k)}$ and $b^k$ to get the coefficient for that term, and then add it to the expansion.

Step 5 ：The final expanded expression using the Binomial Theorem is: $(2x+1{)}^5=32x^5+80x^4+80x^3+40x^2+10x+1$