Question

How many terms are there in the expansion of ${(1+2x+x^2)}^{10}$?

• A. $11$
• B. $20$
• C. $21$
• D. $30$

Answer 1

The correct option is C $21$

Now,

$(1+2x+x^2{)}^{10}=((1+x{)}^2{)}^{10}=(1+x{)}^{20}$

Now, the number of terms in the expansion of $(1+x{)}^n$ are $n+1$.

Thus, the number of terms in the expansion of $(1+x{)}^{20}$ will be $20+1=21$.

Hence, option C is correct.