3.4 Expand (x +a)" for n a positive integer Expand the following: i) (x + 5)3 ii) (x + 3)4 iii) (x + 1)5

Q: 6[5+2(9-4)]

A: Consider the given expression.

Q: Show that for every integer n, n³ + 2 is not divisible by 4.

A: Here, we use rules of divisibility.

Q: In (5 – x) – In (5 + x) = -In 9

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Q: 17. Expand using Pascal's Triangle or the Binomial Theorem. Be sure to show the setup. Then,…

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Q: What are the first and last terms in the expansion of (5x + 4y)*?

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Q: (a) On a certain computer system, a valid password is a sequence of 6 to 8 symbols. The first symbol…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: (n^2-n)+((n-1)^2-(n-1))+....+(1^2-1) =n(n+1)(2n+1)/6 - n(n+1)/2

A: We shall first derive the formulas for sum of first n natural numbers and sum of squares of first n…

Q: Find each (n+3)(n+2) (4n 5)(3n + 2) (n+7)(n + 5)

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: Write the binomial expansion for (x+ 2y)*. (x + 2y)* =D

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Q: ) Find an integer having the remainders 3, 11, 15 when divided by 10, 13, 17, respec- tively.…

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Q: {21} s² +4 9-1 3 (28+5)³ 2} ₁-55

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Q: What is the result of the following operation: (1,10) n (10) (A) 0 B) (1,10) (1,10) (1,10)

A: We have to find the intersection The intersection of two sets is the set of elements that are common…

Q: How many 6-digit numbers have three even and three odd digits? (The first digit cannot be zero.)

A: It is given that a 6-digit number is to be formed which will have three even and three odd digits.…

Q: This will be (n+k-1)= 29+6-1 29 -¹1) = 34 29 = 278, 256.

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Q: How did you found the bounds 2 and 8

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Q: Determine the number of partitions of {1,2,..., 25} in 5 parts, where each part consists of 5…

A: In this question we have to determine the partitions of {1, 2, ....., 25} in 5 parts, where each…

Q: The 4th term in the expansion of (2x² – 3x)* is - 10 Ca (2r²)*(-3z)® O 10 C4 (2a²)°(–3x)“ O 10 C3…

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Q: Write the first 3 terms of the expansion of (3x - ) – 2)" and simplify |

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Q: 3[2+4(5+2*3)]

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Q: 1. Suppose when using the Binomial Theorem an expansion turned out to be the expression as shown…

A: Formula for Binomial theorem: a+bn=an+nan-1b+nn-12!an-2b2+nn-1n-23!an-3b3+.....+bn Given expression:…

Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

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Q: 10 Which term of the expansion of (x²+4) ¹º contains x 20 Term number contains x 20

A: