Perfect+Square+Trinomials

A perfect squre trinomal is when you multiply a binomial by itself.
For Example (x+1) x (x+1) = x 2 + x + x + 1 = x 2 + 2x + 1

Factoring a perfect square trinomial when the middle term is positive.
An equation to keep in mind when factoring perfect square trinomials is a 2 + 2ab + b 2 the first term is a 2 and the base is a the third term b 2 and the base is b
 * you can find the base of the terms by taking the square root of the first and the third term.

Now you put the bases in parentheses with a plus sign in between them since the middle term is positive. (a + b)  Then put it to the second power and your done. (a + b) 2 Example: Given: x 2 + 10x + 25 Base of the first term: x Base of the second term: 5 Parentheses: (x + 5) Final Answer: (x + 5) 2

Factoring a perfect square trinomial when the middle term in negative.
An equation to keep in mind is a 2 - 2ab + b 2 = (a - b) 2 Then you repeat the same steps. Example: Given: x 2 - 18x + 81 Base of first term: x Base of the second term: 9 Parentheses: (x - 9) **You use the sign of the middle term Final Answer: (x - 9) 2
 * remember to find the square roots of the first and last term.

How to check if you have a perfect square trinomial.
First you find the base of the first term and the base of the last term. So in the equation x 2 + 24x + 144

The first base is x The base of the last term is 12 Now you multiply the bases together to get 12x After that you take 12x and multiply it by 2 And since (12x) x 2 = 24x that equation is a perdect square

You can do the same thing for an equation with a middle term that is negative. The only differenece is that after you have multiplied the bases together you multiply it by -2