Answer
$8x^{3}+12x^{2}+6x+1$
Work Step by Step
The standard form of a polynomial is
$a_{n}x^{n}+a_{n}x^{n-1}+\cdots+a_{1}x+a_{0}$
(written in order, highest degree first. If a term is missing, it means that the coefficient is 0)
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Use the perfect cube formula $(A+B)^{3}=A^{3}+3A^{2}B+3AB^{2}+B^{3}$, with $A=2x$ and $B=1$, to obtain:
$(2x+1)^{3}=(2x)^{3}+3\cdot(2x)^{2}\cdot 1+3\cdot(2x)\cdot 1^{2}+1^{3}$
= $8x^{3}+3(4x^{2})+6x+1$
= $8x^{3}+12x^{2}+6x+1$
