(a) Use the Binomial Theorem to write the sum () - ()-()- - ()- 2+ in the form a" for a suitable a E R. (b) Find the constant term (this is the coefficient of z to the power zero) in the expansion of (G-2)".

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: (a) Find the binomial expansion of (1 – x)-1 up to and including the term in x?.

A:

Q: Expand with help of Binomial Theorem (- +)

A: Using the Binomial theorem, the binomial expansion formula for (a+b)n is given by the formula,…

Q: 4. Find the expansion of (x + y)6 using Binomial Theorem.

A:

Q: Зх —1 A B (b) (i) Express (1– x)(2 - 3x) in the form - x 2-3x , where A and B are integers. Зх— 1…

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Q: a. Coefficient of x1/y21 in the expansion of (3x-2y)38 b. Coefficient of x23y41 in the expansion of…

A: The expression, nr can be defined by the formula, nr=n!(n-r)! r! .

Q: (b) (ii) Show that the binomial expansion of(1 + x) + (1-x) up to the term in x² is 2- 16 Hence, by…

A: The binomial expansion of the (1+x)k is given by (1+x)k = 1+kx+k(k-1)2!x2+k(k-1)(k-2)3!x3+........

Q: find the Maclaurin expansion of e-2x In(1+x)

A: fx=e-2xln1+x

Q: 1. Use the binomial theorem to fully expand (x² - 2y)4. Expectations Each term of the full expansion…

A:

Q: Evaluate 4 (1). 4

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Prove the following using the binomial theorem: ()=()+ 2n

A: In this context, the aim is to prove 2n2=2n2+n2.

Q: 3x2 Q1/ A/ Expand with binomial formula: (1- * Q1/B/ Find the value of G? -15 3- 36 = [4 -6 4 -13 -4…

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

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Q: (Vx - V3)° 6.

A: