Question

When the expression (x + 2)^8 is expanded and like terms are combined, what is the coefficient of x^3?

A) 28
B) 56
C) 84
D) 112

Answer 1

When expanding (x + 2)^8, the coefficient of x^3 is 1792.

Step-by-step explanation:

When expanding the expression (x + 2)^8, we can use the binomial theorem to find the coefficients of each term. The binomial theorem states that the coefficient of the term with x raised to the power of k is given by the formula:

C(8, k) * (x^k) * (2^(8-k))

For the coefficient of x^3:

C(8, 3) * (x^3) * (2^(8-3))

Simplifying:

C(8, 3) = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = 8 * 7 * 6 / (3 * 2 * 1) = 56

(x^3) * (2^(8-3)) = x^3 * 2^5 = 32x^3

Therefore, the coefficient of x^3 is 56 * 32 = 1792.