Binomial expansion

Binomial expansion is when you take a special kind of math problem that has two terms (we'll call them A and B) with an exponent (a little number up high like this: A^3).

Now, if someone asks you to expand that binomial expression, what they want you to do is "open it up" so you can see every single term that's hiding inside.

Here's an example of binomial expansion:

(A + B)^2 = A^2 + 2AB + B^2

Let's say we have the problem (3 + 2)^3. We can use the binomial expansion to find the answer by following these simple steps:

1. Write out the formula for binomial expansion: (A + B)^n = A^n + nA^(n-1)B + n(n-1)/2! A^(n-2)B^2 + ... + B^n.
2. Replace A with 3 and B with 2, and n with 3 (which is the exponent we're working with).
3. Write out the expanded form of each term.
4. Simplify the terms and add them together to find the final answer.

So, using the formula we just wrote out...

(3 + 2)^3 = 3^3 + 3(3^2)(2) + 3(3)(2^2) + 2^3

...we can simplify each of those terms:

27 + 54 + 36 + 8

...and add them together:

125

So, the answer to (3 + 2)^3 is 125.

In summary, binomial expansion is a way to find all of the individual terms hiding inside a math problem with two terms and an exponent. By using a special formula and making some substitutions, you can open up the problem and find the answer by simplifying and adding up all the terms.