Consider the given trinomial.
9x^2+6x+1
To determine if an expression is a perfect square trinomial, we need to ask ourselves three questions.
Is the first term a perfect square?
9x^2= 3^2x^2=( 3x)^2 âś“
Is the last term a perfect square?
1= 1^2 âś“
Is the middle term twice the product of 1 and 3x?
6x= 2* 1* 3x âś“
As we can see, the answer to all three questions is yes! Therefore, we can write the trinomial as the square of a binomial. Recall the formula for factoring a perfect square trinomial.
a^2± 2ab+b^2 ⇔ (a± b)^2
Finally, let's factor the given trinomial. Note there is an addition sign in the middle.
9x^2+6x+1 ⇔ ( 3x+ 1)^2
Checking Our Answer
Check your answer âś“
Let's un-factor our answer and compare it with the given expression.
