Before we explain the straightforward way of factoring perfect square trinomials, we need to define the expression

Whenever you multiply a binomial by itself twice, the resulting trinomial is called a perfect square trinomial

For example, (x + 1) × (x + 1) = x

Another example is (x − 5) × (x − 5)

(x − 5) × (x − 5) = x

Now, we are ready to start factoring perfect square trinomials

The model to remember when factoring perfect square trinomials is the following:

a

Notice that all you have to do is to use the base of the first term and the last term

In the model just described,

the first term is a

the last term is b

Put the bases inside parentheses with a plus between them (a + b)

Raise everything to the second power (a + b)

Notice that I put a plus between a and b.

a

Remember that a

Factor x

Notice that x

Using x

the last term is 1

Put the bases inside parentheses with a plus between them (x + 1)

Raise everything to the second power (x + 1)

Factor x

But wait before we continue, we need to establish something important when factoring perfect square trinomials.

. How do we know when a trinomial is a perfect square trinomial?

This is important to check this because if it is not, we cannot use the model described above

Think of checking this as part of the process when factoring perfect square trinomials

We will use example #2 to show you how to check this

Start the same way you started example #1:

Notice that x

Using x

the first term is x

the last term is 12

Now, this is how you check if x

If 2 times (base of first term) times (base of last term) = second term, the trinomial is a perfect square

If the second term is negative, check using the following instead

-2 times (base of first term) times (base of last term) = second term

Since the second term is 24x and 2 × x × 12 = 24x, x

Put the bases inside parentheses with a plus between them (x + 12)

Raise everything to the second power (x + 12)

Factor p

Notice that p

Using p

the first term is p

the last term is 9

Since the second term is -18p and -2 × p × 9 = -18p, p

Put the bases inside parentheses with a minus between them (p − 9)

Raise everything to the second power (p − 9)

Factor 4y

Notice that 4y

(2y)

the first term is (2y)

the last term is 12

Since the second term is 48y and 2 × 2y × 12 = 48y, (2y)

Put the bases inside parentheses with a plus between them (2y + 12)

Raise everything to the second power (2y + 12)

I hope the process illustrated above when factoring perfect square trinomials was easy to follow. Any questions? Send me an email here.