# Question Video: Finding the Middle Term in the Expansion of a Binomial Mathematics

Find the middle term in the expansion of (15π + 3π)Β².

02:19

### Video Transcript

Find the middle term in the expansion of 15π plus three π squared.

Now, first thing weβre gonna do to actually find the middle term of this expansion is to actually rewrite our expression. And Iβve rewritten it as two pairs of parentheses because what weβve got is 15π plus three π squared. So it means that weβve got 15π plus three π multiplied by 15π plus three π. So now, the next stage is to actually expand our parentheses. And in order to do that, what I need to do is actually multiply every term in our first pair of parentheses by every term in second pair of parentheses.

So Iβm gonna start by actually multiplying the first term in each parentheses. So weβve got 15π multiplied by 15π which gives us 225π squared because 15 multiplied by 15 is 225. And π multiplied by π is π squared. Then next, Iβm multiplying 15π by positive three π which will give us plus 45ππ because 15 multiplied by three is 45. And then π multiplied by π is ππ. Okay, great. So weβre finished with 15π in the first parentheses. Now, letβs move on to the second term in the first parentheses.

So now, weβve got positive three π multiplied by 15π. And this, again, gives us 45ππ. Okay, and now we move on to the last term in each of our parentheses. So weβve got positive three π multiplied by positive three π which gives us our last term which is plus nine π squared.

Okay, great. So now, weβve expanded our parentheses. What we need to do is actually simplify. So therefore, this is equal to 225π squared plus 90ππ β because we had 45ππ plus 45ππ, so thatβs 90ππ β plus nine π squared. So now we look back at the question. And the question asked us to find the middle term which we can see is positive 90ππ from our expansion.

So therefore, we can say that the middle term in the expansion of 15π plus three π all squared is equal to 90ππ.