need help asap please and thank you

need help asap please and thank you

In the binomial expansion (a+x)^n where n>4, the coefficient of x^3 is twice that of x^4. 1) Show that n=2a+3 In the same expression, the coefficient of x^2...

using combinations and why.

I have to approximate 0.99^9, using binomial theorem. I can't figure out how to get it to (1 + x)^9 form.

A natural number, x, is called a power of ten if there exists another natural number, y, such that 10^y = x. Show that the set of powers of ten is countably infinite.

Give an example of a cubic (degree 3) function that is bijective. Explain why it is bijective. Give an example of a cubic (degree 3) function that is not bijective. Explain why it is not bijective...

Find and explain a counter example to show that the following statement is false: If a, b ∈ R\Q then ab ∈ R\Q.

The choices are. (a) -2250 (b) -1275 (c) 1275 (d) 2250 (e) -49

Use the Binomial Theorem to expand the following: (a+b)^6 (x+1)^7

use the binomial therom

Use binomial theorem

In the expansion of (2+x)^14 multiplied by (1+2/x)^14, find the coefficient of x^12.

Find the term independent of x in the expansion of (1+x+x-3)7 after the expansion is performed. Note that the answer is 141.

Find the term independent of x in the expansion of (1+x+x-3)7.

If (1+ax+bx2)4=1+8x+32x2+...., find a and b.

Find the specified nth term in the expansion of the binomial. (Round your answer to three decimal places.) (8x + 2y)16, n = 12

Learning about probability and the Binomial Theorem

a. (4x-y)5 b. (5x+y)2 c. (x+√(5/3) y)4 d. (4x+y)5

Please expand :(x+y+z)^(n)

Please expand :(a+x)^(-n)

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