If the coefficient of 4 consecutive terms in the expansion of (1+x)" are a₁, a2, a3, a4 respectively, then show that: 2a3 a1 a3 a₁ + a2 a3 + a4 a2 + = + a3

Q: If n be positive integer, show that the algebraic sum of the numerical coefficients in the expansion…

A: As given above that n be a positive integer. And the given expression is: 3x-2yn We have to prove…

Q: The expansion of (1 - x)® = A 1+4x - 7x² + . B 1- 4x + 7x2 - C 1+ 4x - 7x2 + Đ 1- 4x + 7x² – 23.

A: Please see the explanation below

Q: Determine the coefficient of xaxzx if (x1 + x2 + x3 + x4)1ª is expandec

A: This is given by the multinomial coefficient formula. We state the theorem and then deduce the…

Q: Consider the expansion of x² 10 3

A: Suppose we have binomial expression . Then its expression is as ;                       The general…

Q: What is the coefficient of the following term

A: The binomial expansion of a series is given by the expression (x+y)n=∑k=0nCknxn-kyk. Thus, the…

Q: 1 V91 - 36x +37

A:

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: The fourth term in the expansion (2x – 3) -3 is 270 64x6 O 270 32x6 O 270 64x3 O 540 64x3

A:

Q: Find the coefficient of a3b9 in the binomial expansion of  (36a - 1/6 b)^12

A: Answer

Q: O write the expansion of : (3a+ 2b)$ , (4z – w) , - -→*

A: We have to expand the following expression by using binomial expansion

Q: The constant term in the expansion of the expression 4x is given by 15

A:

Q: Construct the seventh and eighth rows of Pascal’s tri-angle and write the binomial expansions of (x…

A: Pascals triangle: 11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 11 7 21 35 35 21 7 1

Q: Add the polynomials (10z - 82 7æ³ - 10) + (- 4x + 12a + 7a + 9) | Submit Question

A: Add the polynomials. Solution is given below-

Q: Expand (* + 2)x-2)- (x-2) O a x - 4 O b x -x- 6 x - 2x - 4x+ 8 x -x- 2 x - x O c e

A: The given function is x+2x-2-x-2.

Q: In the expansion of (x + y)16 which term has the same coefficient as x14y2? O a. x12,4 Oc x3y14 O d.…

A:

Q: Use the Binomial Theorem to expand: (x- 2y)* a. x* - 8x*y + 24x²y² – 32xy + 16y* b. x* - 16y* c. x*…

A: Expandx−2y4

Q: Write out the first three terms in the expansion of (x + y)^20

A:

Q: Find the coefficient of x24 in (x + x2 + x3 + x4 + x5 )8

A:

Q: What is the coefficient of 8 in the expansion of (x + 1)¹³ + x²(x + 2) ¹6 ? 13

A:

Q: expand 7q(q-2)

A: To expand: 7qq-2 We know that: a(b+c) = ab +ac

Q: 2r2 + 2r + 11 dr 2r +3)(x² + 4)'

A:

Q: Is it true that GCD(6,14,119) x LCM(6,143,119)= 6x143x119?

A: We know that GCD(a,b,c) × LCM(a,b,c) = axbxc

Q: The fourth term in the expansion (2r + y)' is

A: The equation for the combinations n taken r at a time is equal to Crn=n!n-r!r!.  The continued…