How do you factor the expression #c^2+28c+196#?

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Answer 1 · 2016-04-11T05:49:56

# = (c + 14 ) ( c + 14 ) #

#c^2 + 28c + 196#

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 = 1 * 196 = 196 #

AND

#N_1 +N_2 = y = 28#

After trying out a few numbers we get #N_1 = 14# and #N_2 =14#
#14*14 = 196#, and #14+ 14 = 28#

#c^2 + 28c + 196 = c^2 + 14 c + 14c+ 196#

# = c ( c + 14 ) + 14 ( c + 14)#

#(c+ 14)# is a common factor to each of the terms

# = (c + 14 ) ( c + 14 ) #