Question

(X+2) is raised to the fifth power period the third term of the expansion is:

Answer 1

Solution

- The Binomial expansion formula is given by:

$(x+y)^n=\sum_{k=0}^n(^nC_k)x^{n-k}y^k$

- Applying this formula to our expression, we have:

$(x+2)^5=^5C_ox^5(2^0)+^5C_1x^4(2^1)+^5C_2x^3(2^2)+...$

- From the above, we can see that the 3rd term is

$^5C_2x^3(2^2)=C(5,2)x^32^2$

Final Answer

The answer is

$C(5,2)x^32^2\text{ \lparen OPTION 3\rparen}$