Exponents

But first you need to know what an Exponent is.

Here is a quick summary:

An exponent says how many times to use something in multiplication. In this example: 82 = 8 × 8 = 64

A coefficient is a number used to multiply a variable.

Example: 6z means 6 times z, and “z” is a variable, so 6 is a coefficient.

Exponents

An exponent of 1 means just to have it appear once, so you get the original value:

Example: 8¹ = 8

An exponent of 0 means not to use it at all, and we have only 1:

Example: 8⁰ = 1

Exponents of (a+b)

Now on to the binomial.

We will use the simple binomial a+b, but it could be any binomial.

Let us start with an exponent of 0 and build upwards.

Exponent of 0

When an exponent is 0, you get1:

(a+b)⁰=1

Exponent of 1

When the exponent is 1, you get the original value, unchanged:

(a+b)¹ = a+b

Exponent of 2

An exponent of 2 means to multiply by itself:

(a+b)² = (a+b)(a+b) = a² + 2ab + b²

Exponent of 3

For an exponent of 3 just multiply again:

(a+b)³ = (a+b)(a² + 2ab + b²) = a³ + 3a²b + 3ab² + b³

We have enough now to start talking about the pattern.