Factor polynomial $$ 4n^{2}-56n+196 $$

$$ 4n^{2}-56n+196 = 4( n-7 )^{ 2 } $$

Step 1 :

After factoring out $ 4 $ we have:

$$ 4n^{2}-56n+196 = 4 ( n^{2}-14n+49 ) $$

Step 2 :

Both the first and third terms are perfect squares.

$$ x^2 = \left( \color{blue}{ n } \right)^2 ~~ \text{and} ~~ 49 = \left( \color{red}{ 7 } \right)^2 $$

The middle term ( $ -14x $ ) is two times the product of the terms that are squared.

$$ -14x = - 2 \cdot \color{blue}{n} \cdot \color{red}{7} $$

We can conclude that the polynomial $ n^{2}-14n+49 $ is a perfect square trinomial, so we will use the formula below.

$$ A^2 - 2AB + B^2 = (A - B)^2 $$

In this example we have $ \color{blue}{ A = n } $ and $ \color{red}{ B = 7 } $ so,

$$ n^{2}-14n+49 = ( \color{blue}{ n } - \color{red}{ 7 } )^2 $$

Polynomial Factoring Calculator