Recall the formula for the expansion of (a+b)^n stated by the Binomial Theorem.
20c^3d^3
Practice makes perfect
To find the 4^(th) term of the binomial expansion, we should recall the Binomial Theorem. It states that for every positiveinteger n, we can expand the expression (a+b)^n by using the numbers in the n^(th) row of Pascal's Triangle.
It can be shown that the i^\text{th} coefficient of the n^\text{th} row of the Pascal's Triangle equals _nC_i. Therefore, we can restate the binomial theorem using combinations.
Next, let's recall the formula to calculate the combination _nC_x.
_nC_x ⇔ n!/x!(n-x)!
We will use this to substitute the values of the combinations in the formula for the binomial expansion.
