# How do you determine whether #9x^2+6x+1# is a perfect square trinomial?

##### 1 Answer

#### Explanation:

Note that in general:

#(a+b)^2 = a^2+2ab+b^2#

Given:

#9x^2+6x+1#

Note that

So with

#2*3x*1 = 6x" "# - yes

#9x^2+6x+1 = (3x+1)^2#

**Footnote**

If you are familiar with square numbers, then you may recognise:

#961 = 31^2#

Notice that this corresponds to:

#9x^2+6x+1 = (3x+1)^2#

This correspondence is no coincidence. Think about putting

Since the numbers

This can help in general with quickly spotting some perfect square trinomials and other binomial products with small coefficients:

#4x^2+4x+1 = (2x+1)^2" "# like#" "441 = 21^2#

#x^3+3x^2+3x+1 = (x+1)^3" "# like#" "1331 = 11^3#