Question

Use binomial theorem to find the binomial expansion of the expression. (d + 3)^7

Answer 1

There are several methods which method you gonna use?

Answer 2

I don't know how to find this at all, I need a formula or an explanation.

Answer 3

Well, do you know what is binomial theorem?

Answer 4

Ok what I'll do is using this instead, its still expansion but less painful
\[\huge (p+q)^n \\ \\ \huge _n C _r (q)^r(p)^{n-r}\]
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\[_7C_0(d)^0(3)^7=2187 \\ \\ _7C_1(d)^1(3)^6=5103d \\ \\ _7C_2(d)^2(3)^5=5103d^2 \\ \\ _7C_3(d)^3(3)^4=2835d^3\\ \\ ... \\ \\ _7C_7(d)^7(3)^0=d^7\]

Answer 5

945d^2
189d^5
21d^5

Alright, I got it!

Answer 6

\(\large{{(x+y)^n = {{n} \choose {0}} x^n y^0 + {{n} \choose {1}} x^{n-1} y^1 + {{n} \choose {2}} {x^{n-2} {y^2}} +... + {{n} \choose {r} } x^{n-r} y^{r} + {{n} \choose {n}} x^{0} y^n }}\)

The above is binomial theorem formula. Sorry for late response.