Question

The number of distinct terms in the expansion of $(x+yz{)}^{16}$ are

• A. $136$
• B. $153$
• C. $16$
• D. $17$

Answer 1

The correct option is D $17$

We have been given $({x+yz)}^{16}$

$({x+yz)}^{16}$ = ${{}^{16}C}_0{x}^{16}{yz}^0+{{}^{16}C}_1{x}^{15}{yz}^1+..........{{}^{16}C}_{16}{x}^0{yz}^{16}$

Thus, we can see that in each term the powers of the variables $x,y$ and $z$ will be different.

So, there will be $17$ terms and all of them will be distinct.