Question

find the number of terms in the expansion of (2x+3y+z)^7 is​

Answer 1

The number of terms in the expansion of $(2x+3y+z)^{7}$ is 36.

Concept to be used:

• Trinomial. If there are three terms in a polynomial, then it is a trinomial. For example, $p(x)=ax^{2}+bx+c$.

However when we find the power of a trinomial, that is, if we have $(a+b+c)^{n}$, then the number of terms in the expansion is given by

$\boxed{\dfrac{(n+1)(n+2)}{2}}$

Step-by-step explanation:

The given expression is $(2x+3y+z)^{7}$.

Thus, $n=7$.

So, the number of terms in the given expansion is

$\dfrac{(n+1)(n+2)}{2}$

$=\dfrac{(7+1)(7+2)}{2}$

$=\dfrac{8\times 9}{2}$

$=\dfrac{72}{2}$

$=\bold{36}$

#SPJ3