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#