Step 1 :

After factoring out $ 5 $ we have:

$$ 45c^{2}-240c+320 = 5 ( 9c^{2}-48c+64 ) $$

Step 2 :

Both the first and third terms are perfect squares.

$$ 9x^2 = \left( \color{blue}{ 3c } \right)^2 ~~ \text{and} ~~ 64 = \left( \color{red}{ 8 } \right)^2 $$

The middle term ( $ -48x $ ) is two times the product of the terms that are squared.

$$ -48x = - 2 \cdot \color{blue}{3c} \cdot \color{red}{8} $$

We can conclude that the polynomial $ 9c^{2}-48c+64 $ 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 = 3c } $ and $ \color{red}{ B = 8 } $ so,

$$ 9c^{2}-48c+64 = ( \color{blue}{ 3c } - \color{red}{ 8 } )^2 $$

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