expanding brackets

I do not understand this binomial sum thing for (a+b)^n. Surely (a+b)^n=a^n+b^n why is there a need for all this confusing binomial?

(a+b)^n=a^n+b^n is not true in general
e.g. a=1, b=1, n=2 (1+1)^2=2^2=4 not equal to 1^2+1^2=1+1=2

The binomial allows you to expand out (a+b)^n correctly

but your example is wrong

(a+b)^n=(1+1)^2=1^2+1^2=1+1=2

and a^n+b^n=1^2+1^2=2

they are the same I am right
Can someone who knows what they are doing please help?

but your example is wrong

(a+b)^n=(1+1)^2=1^2+1^2=1+1=2

and a^n+b^n=1^2+1^2=2

they are the same I am right
Can someone who knows what they are doing please help?

but your example is wrong

(a+b)^n=(1+1)^2=1^2+1^2=1+1=2

and a^n+b^n=1^2+1^2=2

they are the same I am right
Can someone who knows what they are doing please help?

You have assumed the result when calculating (1+1)^2. You cannot do this.

you used (a+b)^n=a^n+b^n when evaluating (a+b)^n so obviously you are going to get the same thing I could and prove anything doing that eg. orange=bananax x=1 orange=banana*1=banana bananax=banana*1=banana.(a+b)^n a=1 b=1 n=2 = (1+1)^2=2^2=4 not 2.

It is a mathematical formula though so true for all a,b and n.

Its not a mathematical formula, it is a common student mistake.

It is a mathematical formula though so true for all a,b and n.

it is most certainly not!

no offense but your example was wrong so I am hesitant to believe you. Have you actually covered this in class yet?

my example clearly disproves your 'mathematical formula'

However, I cannot be bothered to argue with you. Maybe someone else will help you sort out your life.

so I was right then.

It is always difficult to decide if someone is a troll or has a genuine misunderstanding

I am going to assume that you have a genuine misunderstanding

I assume that you know that $m^2 = m \times m$

From there I assume that you know that $(a+b)^2 = (a+b)(a+b) = a(a+b) + b(a+b) = a^2 + ab + ab + b^2 \not= a^2 + b^2$




Also I assume that you know that 1+1 = 2 and that BIDMAS tells you do evaluate brackets before indices so that $(1+1)^2 = 2^2 = 4$




Both of these demonstrate that your belief that $(a+b)^2 = a^2 + b^2$ is incorrect

Do you reckon they will understand proof by Maclaurin's series?(joke)

Why are you making fun of me

I probably would understand whatever you are talking about - I got an A in GCSE Maths and so I am doing addition maths this year.