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

$= (c + 14 ) ( c + 14 )$

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