How do you factor completely #4c^2 - 12c + 9#?

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Answer 1 · 2016-04-22T16:50:06

# (2c - 3 ) (2c -3) # is the factorised form of the expression.

#4c^2 - 12c + 9 #

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #xc^2 + yc + z#, we need to think of 2 numbers such that:

#N_1*N_2 = x*z = 4 * 9 = 36#

AND

#N_1 +N_2 = y = -12#

After trying out a few numbers we get #N_1 = -6# and #N_2 =-6#
#-6*-6 = 36#, and #(-6)+(-6)= -12#

#4c^2 - 12c + 9 = 4c^2 - 6c - 6c + 9 #

# = 2c(2c -3) -3 (2c - 3)#

#(2c - 3 )# is a common factor to each of the terms

# = (2c - 3 ) (2c -3) #