Question

How many terms are there in the expansion of$\mathbf{(}\mathit{x}\mathbf{+}\mathit{y}{\mathbf{)}}^{\mathbf{100}}$after like terms are collected?

Short answer

After like terms are collected there are 101 terms in the expression.

Step-by-step solution

The given expression is:

$(x+y{)}^{100}$

In the expansion of $\mathbf{(}\mathit{x}\mathbf{+}\mathit{y}{\mathbf{)}}^{\mathbf{n}}$, there are n + 1terms.

Put in the expression of number of terms of

we get

$$\begin{gathered} n+1=100+1 \\ =101 \end{gathered}$$terms.

Thus, there are 101 terms in the expression$(x+y{)}^{100}$ .