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guajiro [1.7K]
3 years ago
7

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

Mathematics
2 answers:
Alja [10]3 years ago
8 0
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
 
aleksandrvk [35]3 years ago
6 0

Answer:

8th term = -721710x⁴y⁷

Step-by-step 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.

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Product of Powers: When you are multiplying like terms with exponents, use the product of powers rule as a shortcut to finding the answer. It states that when you are multiplying two terms that have the same base, just add their exponents to find your answer.

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Quotient of Powers: When you are dividing like terms with exponents, use the Quotient of Powers Rule to simplify the problem. This rule states that when you are dividing terms that have the same base, just subtract their exponents to find your answer. The key is to only subtract those exponents whose bases are the same.

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Step-by-step explanation:

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