# How do you use the Binomial Theorem to expand #(x + y)^5#?

##### 1 Answer

The final answer :

#### Explanation:

The binomial theorem tells us that if we have a binomial (a+b) raised

to the

#(a+b)^n=sum_(k=0)^nc_k^n *a^(n-k)*b^(n)#

where

and is read "n CHOOSE k equals n factorial divided by k factorial (n-k) factorial".

So

we notice that the powers of ** ' a '** keeps decreasing from

**(which representes ' n ') until it reaches**

*5**also* we notice that the power of ** ' b '** keeps increasing from

**untill it reaches**

*zero***at the last term.**

*5*Now the we have to determine the coefficient of each term through the...

first coefficient

second

but the calculation of combinations can be tedious..so fortunately

there is an awesome way to determine the binomial coefficients which is **Pascal's triangle**

it is easy to deduce this triangle :

hope that helps ! : )