a) Obtain the expansion for (3 + 2x)* in ascending powers of x b) Find the term independent of x: 3 G- 5x³ ) 10 x2 c) Obtain the expansion of 1-3x2 up to the term in x8 d) Solve the following: 12 Σ r - 6 r=4

Q: 1) (a) Determine the simplest form of the expansion of (2x4 - 1) 4. 4x (b) Determine the coefficient…

A: Consider,(1) (a) Given,(2x4−4x1​)4use the binomial theorem formula to simplify the given…

Q: Expand and simplify. (8h +3) (7h² – 4h+1) - O 56h3 – 32h² + 8h + 3 - O 56h3 – 11h? 4h + 3 O 56h3 +…

A:

Q: (1+ 2x + 4x? +8x + ...)(3x² + 3x* + 3a° + · . .)(x³ + 2a® + 3x° +

A:

Q: (2x³ 3y) Drag an expression or value into each box to correctly complete the statements. How can you…

A:

Q: The coefficient of x²y4z5 in the expansion of (3x+y+z)¹¹ is

A: The given expression is: (3x + y + z)11 To find: The coefficient of x2y4z5 in the expansion of (3x +…

Q: Find the 5th term in the expansion of x3 7 2y2) x2

A: The expression is  x3-2y2x27

Q: .What is the coefficient of x7 is the expansion of (2x°+)29 ? [if the answer has a form like…

A:

Q: i. Find the coefficient of x in the expansion of ( 2x –÷) . ii. Hence find the coefficient of x in…

A:

Q: Write the fourth term of the expansion of (2x+ 3y)°.

A: We can get desired result by two ways. One is by opening binomial expansion then getting fourth…

Q: ) Write the expansion of (3 + 2x) and use the first three terms of the expansion to approximate3.26.

A: Concept is binomial theoram  3.2 = (3+0.2) 0.2 = 2x0.1

Q: Consider the expansion of (2+x²³²) ¹+¹ ² where 2+2 nt next the coefficient of X² is 1792, Given that…

A:

Q: Answer the following: a) What is the general term of (x-y)xy? b) In the expansion of (1+x)^n the…

A:

Q: Find the coefficient of a?bi in the expansion of (2a - bj)^5

A:

Q: (c) Find the term independent of x in the expansion of, 15 + 4x?

A:

Q: (i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N…

A: Properties of floor functions will be used.

Q: Find the index of 5 relative to each of the primitive roots of 13 (a) 2 (b) 6 (c) 7 (d) 11

A: To find the index of 5 relative to each of the primitive roots of 13. We know that p be prime number…

Q: Compute the constant term in the expansion of (2x³ + ½)¹².

A:

Q: 12 Find the power of x in that term of the expansion of 2+ 2 which has the greatest numerical…

A:

Q: Consider the binomial expansion of (a + x)²0 where a is a rational number. (a) (b) Write down the…

A: NOTE: Refresh your page if you can't see any equations..The binomial theorem is given by,here we…

Q: 2 (a) Work out 14 x 4 – 24 ÷ 2. (b) Find a number between 80 and 90 that is a multiple of both 3 and…

A: We have to solve two subparts in the given problem.                        (a) We need to work out…

Q: What is the coefficent of 5 in (x + 1)7 - x²(x+3) 5

A:

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: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: The Binomial Theorem is, (a+b)n=∑k=0nnkan-kbk Where, nk=n!k!(n-k)! The given question is to find the…

Q: Question 3: Find the coefficient of x4 in the expansion of (1 + x + x²)10 .

A: Introduction :

Q: Prove that n2+n  is  divisible by 2, where nN.

A:

Q: (c) Find the term independent of x in the expansion of, 15 2 +

A:

Q: The binomial theorem states that for any real numbers a and b, (a +b)" = E o (") a"-* for any…

A:

Q: term m (5x + 2) 5; Find the 5th term. O 160 O 1000x² 200x O400x he expansion For question number 22!…

A: