Question

Binomial expansion help!!

calculate the coefficient of x^2y^6 in the expansion of (x+y)^8

Answer 1

\[x^8+8 x^7 y+28 x^6 y^2+56 x^5 y^3+70 x^4 y^4+56 x^3 y^5+28 x^2 y^6+8 x y^7+y^8 \]

Answer 2

So the coefficient of x^2y^6 is 28. right?

Answer 3

So the coefficient of x^2y^6 is 28. right?

Yes.

Answer 4

If you have access to the Mathematica program you will find that it is easier to just ask it to expand (x+y)^8 . Takes 63 millionths of a second for the expansion on a mid 2010 IMac.

Answer 5

Note also that all the coefficients can be found using
$$
\binom{8}{2}=\binom{8}{6}=28
$$
Where 8 is the total power of the term (i.e. 2+6) and 2 is the degree of either of the small terms (2 or 6)

Answer 6

As another example, to determine the coefficient of
$$
x^3 y^5
$$
take
$$
\binom{8}{3}=\binom{8}{5}=56
$$

Answer 7

That makes sense. Thanks for the help @ybarrap and @robtobey

Answer 8

@studygeek15
Learn ybarrap's method if you are restricted to paper and pencil in a test enviornment

Answer 9

yw

Answer 10

@ybarrap

Thank you for the medal.

Answer 11

you deserve it, we both contributed