Middle term? Algebra

Question

What is the middle term in the expansion (2a - 1)6? (little 6)

Answer 1

I'm assuming the "little 6" is an exponent. LOL

 

So you want to expand (2a - 1)^6.

 

The Binomial Expansion Theorem lets you do that, and hopefully without having to grind the whole thing out. And I'm not going to write out the whole expansion. I'm just going straight to the middle. You can look up the formula to see what it looks like.

 

The middle term is

 

(6! / (3! 3!)) (2a)^3 (-1)^3 = -160 a^3

 

Purplemath and Khan Academy are a couple of sites with good detail on the Binomial Expansion theorem. And Wolfram Alpha will let you do a full expansion. Though you might have to simplify the result yourself. Cheers!

 

 

 

 

Answer 2

Using the binomial theorem:

 

it will be (2a)³((-1)³(₆C₃)  where the Binomial Coefficient is 6!/[3!3!] = 20 so when you put it all together it is -160a³.

 

The ₆C₃ can also be found in Pascal's triangle.