Multiplying a binomial by a binomial

The most common way to multiply binomials is what is called the FOIL method

First
Outer
Inner
Last

Let us look at an example

(x+4) (x+1)

These are both binomials, to multiply them we first multiply the first two terms to get x²

Then we still take the first x and multiply it by the outer number: 1, to get x.

So far we have
x² + x

Now we do the inner number: 4

4 times x is 4x

and finally the last number 4 times 1 is 4

So in total we have
x² + x + 4x + 4

which can be simplified by combining the like x terms to

x² + 5x + 4