Evaluate the factorial expression. (5n + 1)! (5n)! (5n + 1)! (Simplify your answer.) (5n)!

Q: expand and simplify (3m+2n)^4 using the binomial theorem.

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Q: a) Write down the first term in the expansion of (x + 4)°. b) Write down the remaining terms in the…

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Q: Process of finding the factors of the mathematical expression 2d2-8d

A: Given expression is 2d2-8d. We have to write the process of finding the factors of the mathematical…

Q: 6 Given A = 4 and B= -7 8 -7 3 -5 5 Find out the value of (AB) if possible without using the product…

A: Solve by matrix

Q: Using the binomial theorem expression to expand (4a+7b)^8, what would you substitute for the values…

A: Given: (4a + 7b)8

Q: Binomial expressions can differ by a factor of -1. Factor -1 from one of the denominators to…

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Q: Sp-3 2x If there are 23 terms in the expansion of ху then the value of p is

A: We will find out the required value of p.

Q: Expand the binomial using Pascal's Triangle and the Binomial Theorem. 14. (x + 2)5 15. (2x + y)* 16.…

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Q: – })* Q7. In the binomial expansion of (2 written in terms of descending powers of x, find: a. The…

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Q: Expand the binomial using Pascal's Triangle and the Binomial Theorem. 16. (k + 13)5 17. (5m – - n)³…

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Q: The coefficient of x³in the binomial expansion of (2– 3x) is A -1080 26. /B 1080 C -360 D 360

A: we have to find out the coefficient of x3 for function  (2-3x)5

Q: 3a² - 4a – 4 factors to (3a+2}{(a-3).

A: Given polynomial,  3a2-4a-4

Q: (n° - 11n +17n + 16) divided by (n- 3)

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Q: Using the expansion for the binomial: (x° + y°)° : 5.,12 We wish to find the coefficient for the…

A: The formula for binomial expansion is x+yn=∑r=0nCrnxn−ryr. The combination formula isnCr=n!n−r!r!.

Q: 3. Multiply the binomials 3e – 1 and 2e +5 together. Simplify fully.

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Q: 1. Consider the algebraic expression 6n³-n²+5 -11 a. How many terms are there? b. Identify the…

A: As per our guidelines we will only solve the first three subparts i,e a.b.c of question number 1. If…

Q: A 3. What is the value of the 3rd term of the expansion (3y- 2)'? 35a b3 -10206y 20412y O 21a b?

A: Given query is to find the the third term of the expression.

Q: 4 a) (x² + b) (- x*)*

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Q: You are told that the following two statements are true: If Alex is a student, then Alex reads a…

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Q: (n - 11n +17n + 16) divided by (n– 3) n2 - 8n-6, remainder -6 n- 8n - 7, remainder |

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Q: n (x - 1)" The sixth term of the expansion of x is 1287 8 X 3125 . Determine n.

A: Let us consider the expression a+bn. The binomial expansion of the given expression is , a+bn=C0n…

Q: Expand the following using the Binomial Theorem and Pascal’s triangle. Show your work. (x + 2)6 (x…

A: Since you have posted multiple subparts question in this question so i have solved first three parts…

Q: Which of the following is the factor of P(b) = 2b4 + 5b³– 8b² -17b -6 а. b-1 Determine the value of…

A: Given  (a) P(b)=2b4+5b3-8b2-17b-6 (b)G(t)=t2+kt+24 with factor t-3

Q: Which of the following is a false statement? In the expansion of (a +b) the coefficient of a b° is…

A: We have to choose the false statement.

Q: a) Write down the first term in the expansion of (x - 4)5 [Hint: Care is needed with the negative 4]…

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Q: a.Find the expansion of (2+z)5 and write the coefficient of z?. b.Find the expansion of (2+3z+z?)5…

A: We have to expand the polynomials which is given in question And we have to find out the coefficient…

Q: If a_1=8a1​=8 and a_n=-3a_{n-1}an​=−3an−1​ then find the value of a_4a4

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Q: In the expansion of a binomial (a + b)" the third term is equal to 56 the fourth term is 70 and the…

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Q: Solve the recurrence: an= 3an-1+ (2n-5), ao=1

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Q: Which of the following is the value of the coefficient y on the right side of the equation given…

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Q: The table represents the multiplication of two binomials. What is the value of A? 3x -3x A |-3x 10…

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Q: . Factorize the expression (5 - i)z2 - (3 - 2i)z + e2pie(i)

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Q: polynomial p(x) is divisible by the given binomial x-c. 1. p(x)= x^3+6x^2+11x+6, x+1 2. p(x)=…

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Q: Evaluate the factorial expression. (2n + 1)1 (2n) (2n + 1)1 (2n)! (Simplify your answer.)

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Q: 1×2×3x4x.(n–1) The expression gives a re- mainder of (n –1) if n is prime.

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Q: algebriac proof of 8x+12=52

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Q: In the expansion of a binomial (a + b)" the third term is equal to 56, the fourth term is 70, and…

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Q: Expand the following using the Binomial Theorem and Pascal’s triangle. Show your work. (x + 2)6 (x…

A: Given: 1. x+26 2. x-44 3. 2x+35

Q: m - n Fill in the blanks to show that = -1 by factoring out -1 from each term in the numerator. n -…

A: We will sovle this question to using taking common factor.

Q: The Binomial The orem states: -- 2. Catb) n 2 ab' n-/ Find the first five terms in the expansion of…

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Q: 3. Which of the following binomial is a factor of P(x) = 2x³ + 7x² + x – 10? %3D A. В. 2x + 1 C. x+4…

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Q: Hareem takes a medicine to control his blood pressure. He takes a 25 mg pill in the morning. Suppose…

A: Hareem takes a medicine to control his blood pressure. He takes a 25 mg pill in the morning.…

Q: -4+-10+-16+.,t-58 sum: Find the

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Q: 38. What is the coefficient of the 4th term in the expansion (2y -3x)*? a. -216 b. -96 с. 81 d. 216

A: We have to find the 4th term in the expansion 2y-3x4 We can use binomial theorem to find the 4th…

Q: 2. For all positive integer n, the expression n -n+ 3 is always divisible by A) 6 only B) 2 and 3…

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Q: Which of the following is the value of the x coefficient on the right side of the equation given…

A: 4th power expansion (x+y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4

Q: When converting repeating decimals into fractions, is it possible to sometimes get a fraction that…

A: Note: As there are two separate questions posted, we will answer the first question according to…

Q: 4 Find the coefficient of the given term when the expression is expanded by the binomial theorem…

A: Find the coefficient of x2y7 in (2x+3y)9 using binomial expression.