13. Expressing the binomial coefficients in terms of fac- Morials and simplifying algebraically, show that torials n-r+1 (a) (b) n n r r (H) (₁².₁); · (^= ¹); n n-r r r n = n (-(¹)-+ (₁) =

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: When multiplied out, what are the first 4 terms of (x + 3y)0?

A:

Q: 3. (a) Use the Binomial Theorem to expand and simplify (3a²-4b)6

A:

Q: Which binomials are correct for the roots 7 and -2? F oudy O (x-7)(x-2) O (x + 7)(x-2) O (x+7)(x+2)…

A: The given roots are 7 and -2.

Q: Find the following products by using the special binomial products formulas.

A: (a) 5x+12=5x+15x+1=25x2+5x+5x+1=25x2+10x+1

Q: 10. Use the binomial theorem to evaluate (2r³ - y) 5.

A:

Q: 2.xxX-Y) (xX+1)

A: This is the problem of multiplying binomial. It has been done step by step. See the attached image

Q: Find the product of the real numbers  7/19*12/331*(-38/7)=

A: First we multiply the numerators and the denominators straight away, then we reduce the fraction.…

Q: Use binomial theorem to find the constant term (x-1/x)*8

A:

Q: -Expand fully and simplify, (3-x²)5

A: To expand fully and to simplify the following expression.3-x25

Q: What is the formula for calculating binomial coefficients?

A: The binomial coefficient is represented in following ways and it is read as n choose k.

Q: how does (root2)^n come about

A: We show that how  (√2)^n has come out. The rest of the part of solution is correct

Q: Use the binomial theorem to show that 72 Σ(1) ( **(?). i-0 0.

A: Use binomial theorem to show that given formula.

Q: Differentiate the following: (a) (2x – 1)*. (b)(5x + 1)* (3 – 2x)* -

A:

Q: Q4 Derive a recursion for q-binomial coefficients and use it these are polynomials with non-negative…

A: Let us suppose 0<k<n then, nkq-n-1k-1q=qn-1qk-1-1n-1k-1q=qkqn-k-1qk-1-1n-1k-1q  =qknk-1q

Q: Using the binomial theorem to find the 4th term of √x + 2

A:

Q: Jse the Binomia expression (3x + 2y²)°. Show your work. Theorem to expand the

A:

Q: Define binomial coefficient.

A: Binomial Coefficient:- The binomial coefficient in combinatorics is used to represent the variety…