Answer
$240x^4y^2$
Work Step by Step
Our aim is to find the third term for $(2x+y)^{6}$.
General formula:$(p+q)^n=\displaystyle \binom{n}{k}p^{n-k}q^k$
and $\displaystyle \binom{n}{k}=\dfrac{n!}{k!(n-k)!}; k=2$
Now, $(2x+y)^{6}=\displaystyle \binom{6}{2}(2x)^{6-2}(y)^2$
This implies,
$=\dfrac{6!}{2!(6-2)!}(2x)^{4}(y)^2$
$=\dfrac{6 \times 5 \times 4!}{2 \times 1(4!)}(2x)^{4}(y)^2$
Thus,
$=240x^4y^2$
