Thread: Finding a term in a Binomial Expansion

1. Finding a term in a Binomial Expansion

Good evening forum I am having a problem with the following problem any help would be appreciated:

thank you , AC

2. Originally Posted by AlgebraicallyChallenged
Good evening forum I am having a problem with the following problem any help would be appreciated:

thank you , AC
use the binomial expansion formula for $\displaystyle (x + y)^8$

we have $\displaystyle (x + y)^8 = \sum_{k = 0}^8 {8 \choose k}x^{8 - k}y^k$

if we choose $\displaystyle x = a$ and $\displaystyle y = -b^3$ we realize that we want the term where we have $\displaystyle y^3$...that's where k = 3

this is the term $\displaystyle {8 \choose 3}x^5y^3$

note that $\displaystyle {n \choose k} = _nC_k = \frac {n!}{k!(n - k)!}$

3. Originally Posted by AlgebraicallyChallenged
Good evening forum I am having a problem with the following problem any help would be appreciated:

thank you , AC
$\displaystyle (a-b^3)^8 = {8\choose0}a^8 + {8\choose1}a^7(-b^3) + {8\choose2}a^6(-b^3)^2 + {8\choose3}a^5(-b^3)^3 + ...$

see the term you need to find?