Write the binomial expansion for $(x+2)^{3}$.

Step 1 ：The binomial expansion theorem states that any power of the sum of two numbers can be expressed as a sum of products of the two numbers, with coefficients determined by the binomial coefficients. The binomial coefficients for a power of n are the numbers in the nth row of Pascal's triangle. For \((x+2)^{3}\), the coefficients are 1, 3, 3, 1. The terms in the expansion are of the form \(a*x^{b}*2^{c}\), where a is the coefficient, b is the decreasing power of x, and c is the increasing power of 2.

Step 2 ：The binomial expansion for \((x+2)^{3}\) is \(x^{3} + 6x^{2} + 12x + 8\)

Step 3 ：Final Answer: The binomial expansion for \((x+2)^{3}\) is \(\boxed{x^{3} + 6x^{2} + 12x + 8}\)