Answer :
Final answer:
To find the 3rd term of (x + 2)^8, we use the binomial theorem, yielding the term 28 times x^6 times 4 which simplifies to 112x^6. Therefore, the correct answer is option C: 112x^6.
Explanation:
To find the 3rd term of the expansion (x + 2)^8, we can use the binomial theorem. The binomial theorem tells us that the kth term of the expansion of (a+b)^n is given by[tex]C(n, k-1) t imes a^{n-(k-1)} times b^{k-1},[/tex] where C(n, k) is the binomial coefficient, calculated as n! / ((n-k)!k!).
In this case, we are looking for the 3rd term where a is x, b is 2, and n is 8. So the term's order k is 3, meaning we need to find [tex]C(8, 2) times x^{8-2} times 2^{2}[/tex]. Calculating the binomial coefficient C(8, 2) gives us 28, and raising 2 to the power of 2 gives us 4.
Combine these to get the 3rd term: [tex]28 times x^6 times 4 = 112x^6.[/tex]
Thus, the 3rd term of the expansion is [tex]112x^6[/tex], which corresponds to option C.
Answer:
C
Step-by-step explanation:
The general formula for the binomial expansion is
(n over k) * (x)^(n - k) * y^k
n = 8
k = 2 which is the third term. That's because k starts at 0.
n over k = n C k = 8 C 2 = 8!/(8-2)! * 2!
2^2 = 4
n over k = 8!/(6!)(2!) = 8*7 / 2 = 28
x^(n - k) = x^(8 - 2) = x ^6
So the result is
x^6 * 28 * 2^2
112 x^6
The answer is C
