Expand this Binomial!

Probability Level 1

Find the total number of terms of $(x+y)^{63}$ when the expression is expanded.

2 solutions

Swapnil Das
May 20, 2016

The number of terms in the binomial expansion of positive integral index $n$ is $n+1$ .

$\therefore$ $z$ contains $63+1=64$ terms.

It's surprising to see that only 17% people got it correct.

Rohit Udaiwal - 5 years ago

It is now $33\%$ , which means one third. My god.

Swapnil Das - 5 years ago

Lol it's continuously increasing :P

Rohit Udaiwal - 5 years ago

@Rohit Udaiwal – But still can't be 100 :P

Swapnil Das - 5 years ago

@Swapnil Das – now it is 52 :P

A Former Brilliant Member - 5 years ago

@A Former Brilliant Member – I'm your $9^3$ th follower :3

Rohit Udaiwal - 5 years ago

@Rohit Udaiwal – lol. I guess I cannot follow any more.

A Former Brilliant Member - 5 years ago

@A Former Brilliant Member – You are following the whole community,I guess!

Rohit Udaiwal - 5 years ago

Hung Woei Neoh
May 20, 2016

If you did not know the theorem in the other solution, you can try out a few smaller expansions:

$(x+y)^2 = x^2 + 2xy + y^2\\ (x+y)^3 = x^3 + 3x^2y + 3xy^2 + y^3\\ (x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4$

Notice that for each $(x+y)^n$ , the expansion will have a total of $n+1$ terms.

Therefore, $z=(x+y)^{63}$ has $63+1 = \boxed{64}$ terms