one of the terms in the expansion $\displaystyle (x+3)^7$ is $\displaystyle kx^5$. determin the value of k.
$\displaystyle (x+y)^{1}=x+y$
$\displaystyle (x+y)^{2}=x^{2}+2yx+y^{2}$
$\displaystyle (x+y)^{3}=x^{3}+3yx^{2}+3y^{2}x+y^{3}$
$\displaystyle (x+y)^{4}=x^{4}+4yx^{3}+6y^{2}x^{2}+4y^{3}x+y^{4}$
The pattern of coefficients is like pascals triangle, the outside is always 1's and you add the two coefficeints in the line directly above to get the inside ones:
...1 1
..1 2 1
.1 3 3 1
1 4 6 4 1
As for the 3 (or y value see above) when you are talking about a power of 7 the power of the y will always be 7 - power of x in that part of the polynomial.
Try to figure it out and post the solution if you can't get it or if you want me to check it I will give the answer.