Question

The equation shows the beginning of a problem using the Binomial Theorem to expand a power of a binomial.

(a+b)3= _[blank]_

Which equation correctly fills in the blank to complete the Binomial Theorem?

∑3k=0(3k)a3−kbk=1a3+3a2b+3ab2+1b3
∑3k=1(3k)a3bk=3a3+1a2b+1ab2+3b3
∑3k=0a3−kbk=1a3+2ab2+1b3
∑3k=0(k3)a3bk=1k3+3k2b+3kb2+1b3
(3k)a3−kbk=1a3+4a2b+6ab2+4b3

Answer 1

Better take another look at Pascal's Triangle.
for (a+b)^3 the coefficients are 1,3,3,1 not 1,4,6,4
The rows always start and end with 1.

and your notation is very hard to parse.