shortcut for exponential problem

[latinlioness08]

The coefficient in front of the x^5 term in (x+2)^7 is:
a. 21
b. 7
c. 42
d. 84

I know the answer is d. However, to aquire this answer I had to literally FOIL the entire thing. I took it to (x^4+ 8x^3+24x^2+32x+16)(x^3+6x^2+12x+8) before i knew how to tell what the answer was. Is there some shortcut to know what the coefficient in front of the x^n term is in a basic expression like this?

[stapel_eliz]

Is there some shortcut to know what the coefficient in front of the x^n term is in a basic expression like this?

Yes, there is a shortcut. It's called "the Binomial Theorem".

[latinlioness08]

Got it:) Thanks!