Square of a binomial x^2+2x+1

To put an equation into (x+c) ^2, we need to see if the trinomial is a perfect square.

General form of a trinomial: ax^2+bx+c

If c is a perfect square, for example (1) ^2=1, 2^2=4, that's a good indicator that it's a perfect square trinomial.

Here, it is, because 1 is a perfect square.

To ensure that it's a perfect square trinomial, let's look at b, which in this case is 2.

It has to be double what c is.

2 is the double of 1, therefore this is a perfect square trinomial.

Knowing this, we can easily put it into the form (x+c) ^2.

And the answer is: (x+1) ^2.

To do it the long way:

x^2+2x+1

Find 2 numbers that add to 2 and multiply to 1.

They are both 1.

x^2+x+x+1

x (x+1) + 1 (x+1)

Gather like terms

(x+1) (x+1)

or (x+1) ^2.