Identity (mathematics)

Imagine you have a bunch of things like apples or toys that look different but have the same value or worth. These things are what mathematicians call "variables" or "symbols." When we group these variables or symbols together using signs like + or -, we call them "expressions."

Now, an identity is a statement that tells us something that is always true, no matter what kind of variables or symbols we use in our expressions. It's like a rule that we can always rely on.

For example, let's say we have two expressions: (3 + 2) and (5). We can see that these expressions are the same because 3 + 2 equals 5. So we can write an identity that says:

(3 + 2) = (5)

This identity tells us that no matter what variables or symbols we use in our expression, as long as they all have the same value, 3 + 2 will always be equal to 5.

Another example of an identity is the distributive property. This is the rule that says if we have two expressions, like (3 + 2) and 4, and we want to multiply them together, we can distribute the 4 to each term in the parentheses. This gives us:

4(3 + 2) = (4 x 3) + (4 x 2)

This identity tells us that we can always use the distributive property to simplify multiplication problems, no matter what variables or symbols we use in our expressions.