peanutcoco2000
contestada

Determine the most efficient way to use the Binomial Theorem to show the following. (11)^4= 14641
A)Write 11=5+6 and expand.
B) Write 11= 10+1 and expand.
C) Write 11= 3+3+2 and expand.
D)Write 11= 4+4+3 and expand.

Respuesta :

TheHero
Write (1+10) and expand. As you will have nCr *(10)^(n-r)
Where r index n count ( less terms)

The formula for binomial theorem is

[tex](a+b)^n=( \left \ {{n} \atop {0}} \right.)a^{n}+( \left \ {{n} \atop {1}} \right.)a^{n-1}b+( \left \ {{n} \atop {0}} \right.)a^{n-2}b^2+...+( \left \ {{n} \atop {n}} \right.)b^n[/tex]

Now this shall be very easy if the value of a = 1

The formula shall become

[tex](1+b)^n=( \left \ {{n} \atop {0}} \right.)1^{n}+( \left \ {{n} \atop {1}} \right.)1^{n-1}b+( \left \ {{n} \atop {0}} \right.)1^{n-2}b^2+...+( \left \ {{n} \atop {n}} \right.)b^n[/tex]

Which shall be

[tex](1+b)^n=( \left \ {{n} \atop {0}} \right.)+( \left \ {{n} \atop {1}} \right.)b+( \left \ {{n} \atop {0}} \right.)b^2+...+( \left \ {{n} \atop {n}} \right.)b^n[/tex]

So to find 11^4

We must break it as 1 + 10.

Option B) is the right answer.

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