How do you factor the expression $n^2 - 28n + 196$ ?

Question

1213 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-05T16:52:56

$color(blue)( (n-14) (n-14)$ is the factorised form of the expression.

$n^2-28n+196$

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

In this technique, if we have to factorise an expression like $an^2 + bn + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 1*196 = 196$

AND

$N_1 +N_2 = b = -28$

After trying out a few numbers we get $N_1 = -14$ and $N_2 =-14$

$-14*-14 = 196$ , and $(-14)+(-14)= -28$

$n^2-28n+196 = n^2-14n - 14n+196$

$= n (n-14) -14(n-14)$

$color(blue)( (n-14) (n-14)$ is the factorised form of the expression.

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