Question

(x + 2) is raised to the fifth power. The third term of the expansion is:C(5,3)x322C(5, 3)x223C(5, 2)x322

Answer 1

Remember that according to the binomial theorem, the expression that gives the expansion of a binomial (a+b) raised to the nth power is:

`(a+b)^n={\displaystyle \sum_(k=0)^n{C(n,k)a^(n-k)b^k}}`

The first term can be obtained plugging in k=0, the second term by plugging in k=1 and the third term by plugging in k=2. Then, the third term of (x+2)^5 is given by the expression that results after setting n=5, k=2, a=x and b=2:

`\begin{gathered} C(n,k)a^(n-k)b^k \\ \Rightarrow \\ C\left(5,2\right)x^(5-2)2^2=C\left(5,2\right)x^32^2 \end{gathered}`

Therefore, the correct choice is:

`C(5,2)x^32^2`