Question

Find the term in x³in the expansion of (x - 3)⁸

A) -13608x³
B) 13608x³
C) -13608x⁵
D) 13608x⁵

Answer 1

To find the term in x³ in the expansion of (x - 3) ⁸, we can use the binomial theorem and the formula (n choose k) * a^(n-k) * b^k. Plugging in the values x and -3 in this formula, the term in x³ will be -13608x⁵.

Step-by-step explanation:

To find the term in x³ in the expansion of (x - 3) ⁸, we can use the binomial theorem. The binomial theorem states that the term in xⁿ in the expansion of (a + b) ⁿ can be found using the formula:

(n choose k) * a^(n-k) * b^k

In this case, a = x and b = -3. So, the term in x³ will be:

(8 choose 3) * x^ (8-3) * (-3) ^3 = 56 * x^5 * (-27) = -1512 * x^5

Therefore, the correct answer is option C) -13608x⁵.