How do you factor #x^2 + 6x + 9#?

1 Answer
Jun 24, 2015

# color(green)((x+3)(x + 3) #

Explanation:

# x^2+6x+9#

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like #ax^2 + b + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1* 9 = 9#
AND
#N_1 +N_2 = b = 6#
After trying out a few numbers we get #N_1 = 3# and #N_2 =3#
#3*3 = 9#, and #3+3= 6#

# x^2+6x+9#
# =x^2+3x + 3x+9#

# =x(x + 3) + 3(x+3)#

# =color(green)((x+3)(x + 3) #