Question

Find the term indicated in the expansion. (x - 3y)11; 8th term

Answer 1

8th term = -721710x⁴y⁷

Explanation:

Given Binomial is (x - 3y)¹¹

To find the particular term from expansion of binomial, The (a + 1)th term of the binomial expansion of (x + y)ⁿ is:

(a + 1)th term = ⁿCₐ xⁿ⁻ᵃ yᵃ

We need to find 8th term.

So, a+1 = 8

a = 8-1 = 7th term

8th term = ¹¹C₇ x¹¹⁻⁷ (-3y)⁷

8th term = 330x⁴(-3)⁷y⁷

8th term = -721710x⁴y⁷

That's the final answer.

Answer 2

The term in the expansion:
T ( k+1) = n C k * A^(n-k) * B^k.
In this case: n = 11, k + 1 = 8, so k = 7.
A = x, B = - 3 y
T 8 = 11 C 7 * x^(11-7) * ( - 3 y )^7 =
=( 11 *10 * 9 * 8 * 7 * 6 * 5 ) / ( 7 * 6 * 5 * 4 * 3 * 2 * 1 )* x^4 * ( - 2,187 y^7 ) =
= 330 * ( - 2,187 ) x^4 y^7 = - 721,710 x^4 y^7
Answer: The 8th term in expansion is