Help Binomial Question (2 Viewers)

[MyHeadee]

Struggling

 

[Life'sHard]

My g Eddie Woo never fails me

 

[CM_Tutor]

Make sure that you understand how these questions work as they can be given in different forms that cause major difficulties if a wrote-learned algorithmic approach does not match the question form.

 

[ExtremelyBoredUser]

My g Eddie Woo never fails me

facts hes the goat

 

[notme123]

Make sure that you understand how these questions work as they can be given in different forms that cause major difficulties if a wrote-learned algorithmic approach does not match the question form.

how else can this question be asked? it seems the method would always be the same

 

[Undefined]

When looking at the HSC past questions and Baulkham Hill's 2020 year 11 ext yearly the types of ways the question can be asked are:
1. constant term
2. coefficient of specific index
3. coefficient of x^3 in (1 + x + x^2)^5
4. I don't even know how to summarise the next question.

 

[notme123]

When looking at the HSC past questions and Baulkham Hill's 2020 year 11 ext yearly the types of ways the question can be asked are:
1. constant term
2. coefficient of specific index
3. coefficient of x^3 in (1 + x + x^2)^5
4. I don't even know how to summarise the next question.
View attachment 32064

For 3., i know you can make it binomial through grouping but whats a more efficient method

 

[Life'sHard]

For 3., i know you can make it binomial through grouping but whats a more efficient method

There is a method, I just don't know how to explain it without having to learn latex to type it out lol.

 

[Wizjaro]

For 3., i know you can make it binomial through grouping but whats a more efficient method

Use Combinatorics

 

[notme123]

Use Combinatorics

how exactly? i know the binomial expansion if thats what youre referring to

 

[notme123]

the eddie woo method doesnt work for the second one unless i am clincally idiotic can someone pls help me?

 

[ExtremelyBoredUser]

the eddie woo method doesnt work for the second one unless i am clincally idiotic can someone pls help me?

Are you referring to this post?

https://boredofstudies.org/attachments/screen-shot-2021-09-11-at-11-34-10-am-png.32061/

If so, I'm not finding anything wrong? I tried manually and the coeff I got is larger than other values of k. Or maybe you're talking about the other question, if so my bad.

 

[Life'sHard]

how exactly? i know the binomial expansion if thats what youre referring to

Malaysian lad can carry this explanation. It's pretty rare to see these kinds of questions.

 

[notme123]

Malaysian lad can carry this explanation. It's pretty rare to see these kinds of questions.

ok good thats what i was thinking. thank you

 

[notme123]

Are you referring to this post?

https://boredofstudies.org/attachments/screen-shot-2021-09-11-at-11-34-10-am-png.32061/

If so, I'm not finding anything wrong? I tried manually and the coeff I got is larger than other values of k. Or maybe you're talking about the other question, if so my bad.

yes thats correct the second one isnt working for me lol ill try again

I keep on getting

 

[ExtremelyBoredUser]

yes thats correct the second one isnt working for me lol ill try again

Yeah maybe you did the expansion wrong or something? Could someone else looking at this thread double check.

 

[ExtremelyBoredUser]

yes thats correct the second one isnt working for me lol ill try again

I keep on getting

I'm not sure why you're getting that. Could you send your working out?

 

[notme123]

I'm not sure why you're getting that. Could you send your working out?

I do the C(Tr) > C(Tr+1) thing and rearranged for r (keeping the negative in mind as well)

 

[ExtremelyBoredUser]

Alright, I'll upload my working out. I'll use my phone since its quicker. Someone check it because Binomial and Combinatorics aren't exactly my strong suit.

 

[ExtremelyBoredUser]

Apologies for my working out, I just quickly rushed solving the problem.

For some faded parts:
In line 2: - 10!/k!*(10-k)!, in this line i also cancelled out the negatives

On that note, I also struggle with this topic a bit so if anyone in the forum could answer this;

How do you know which term is a and b in the binomial expansion? Sometimes the formula works if the a term is the coefficient of x and vice versa. I'm confused by that so if someone could clarify that, it would be nice.