Answer
$=16x^4+32x^3+24x^2+8x+1$
Work Step by Step
Binomial Theorem or Binomial expansion can be defined as:
$(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$
Need to apply the formula to get the Binomial Expansion.
we have
$(2x+1)^4=\displaystyle \binom{4}{0}(2x)^4(1)^0+\displaystyle \binom{4}{1}(2x)^3(1)^1+\displaystyle \binom{4}{2}(2x)^2(1)^2+\displaystyle \binom{4}{3}(2x)^1(1)^3+\displaystyle \binom{4}{4}(2x)^0(1)^3$
$=(16)(x^4)(1)+(4)(8x^3)(1)+24x^2+8x+(1)1$ $\bf{(Simplify)}$
$=16x^4+32x^3+24x^2+8x+1$
