Precalculus Write down the expansion of three terms

[PeachBlossom]

Hi I know how to solve with two terms, when it is (a+b)^6 example with bionomial theorem. Now I need to solve with three terms. I get confused.

I get the wrong answer all the time, here is how I tried to solve it and picture on the question, it's question a).

Please help me understand what I'm doing wrong, thanks in advance!

 

[PeachBlossom]

The answer, how it should look like.

 

[Harry_the_cat]

0! = 1 not 0.
Also, 2÷0 does not equal 2.

 

[PeachBlossom]

Thank you so much now I solved it got a little bit tired I think so started to make small mistakes.

 

[Steven G]

2÷0 does not equal 2.

Seriously? After all these years I finally realized why I make so many arithmetic mistakes! No more going to the corner for me!

 

[pka]

Seriously? After all these years I finally realized why I make so many arithmetic mistakes! No more going to the corner for me!

What you should know is that by definition purely for connivance \(\displaystyle \bf 0!=1\).
Therefore for \(\displaystyle n>0\) then \(\displaystyle \binom{n}{0}=\dfrac{n!}{0!(n-0)!}=1\)

 

[Steven G]

What does that have to do with my statement (joke) about not knowing that 2÷0 does not equal 2.

For the record, I do know that 0! is defined to be 1 for convenience.