Trinomial expansion

Hi there! Today we're going to learn about something called trinomial expansion.

Have you ever done multiplication before? Great! Trinomial expansion is like a big multiplication problem, but instead of multiplying two numbers together, we're multiplying three expressions together.

But first, let's talk about what an expression is. An expression is just a group of numbers, variables, and symbols (like plus or minus signs) that go together.

For example, if we have the expression (2x + 3), that means we have two times x (which is a variable that can stand for any number) plus 3.

Now, let's imagine we have three expressions that we want to multiply together. Let's call them a, b, and c.

When we multiply a, b, and c together, we get something called a trinomial. A trinomial is just a big expression made up of three smaller expressions that have been multiplied together.

The trinomial that we get when we multiply a, b, and c together will look like this:

abc + ab(c) + a(bc) + (a)bc

Now, let's break down what each part of this trinomial means.

The first part, abc, means that we're multiplying all three expressions together.

The second part, ab(c), means that we're multiplying the first two expressions (a and b) together, and then multiplying that result by the third expression (c).

The third part, a(bc), means that we're multiplying the first expression (a) by the second part of the expression (bc).

And finally, the fourth part, (a)bc, means that we're multiplying the first part of the expression (a) by the last two parts (b and c).

So there you have it! Trinomial expansion is just a fancy way of saying that we're multiplying three expressions together and getting a big trinomial.