How Does the Binomial Theorem Explain the Middle Term of (a+b)^4?

[morbello]

Could you tell me how this equation works and how to get to the answer.ive done it before and am still stuck on how 6a^2b^2 is in the middle

(a+b)^4



a^4 4a^3b

giving the 6A^2B^2 in the middle is it if you have a exponent out side the brackets it works down to ^2 as it would look like or is there an easyer way to say how to do this equation.

is there a formula to work it out.

The Attempt at a Solution

 

[NascentOxygen]

Could you tell me how this equation works and how to get to the answer.ive done it before and am still stuck on how 6a^2b^2 is in the middle

(a+b)^4

First, I should point out that there is no equals sign to be seen anywhere, so you haven't shown us an equation. What you show is an expression.

Are you wanting to express (a+b)⁴ without brackets?

If so, then it's straightforward. You need a large sheet of paper, a sharp pencil, and an eraser.

(a+b)⁴ can be written out as (a+b) (a+b) (a+b) (a+b)

You then work this out in stages, or however you like, e.g., you could do it as:

(a² + 2ab + b²)(a² + 2ab + b²)

Now, multiply this out, one term at a time, and eventually collect terms. There is a lot of writing to do, but each small step is easy. First, everything contained in the second brackets is multiplied by a², then everything in the second brackets is multiplied by 2ab, and so forth.

 

[eumyang]

a^4 4a^3b

Looks like some terms (and operation symbols) are missing.

is there a formula to work it out.

Yes. Look up the Binomial Theorem.