Step 1 :

After factoring out $ 10 $ we have:

$$ 250y^{2}+800y+640 = 10 ( 25y^{2}+80y+64 ) $$

Step 2 :

Both the first and third terms are perfect squares.

$$ 25x^2 = \left( \color{blue}{ 5y } \right)^2 ~~ \text{and} ~~ 64 = \left( \color{red}{ 8 } \right)^2 $$

The middle term ( $ 80x $ ) is two times the product of the terms that are squared.

$$ 80x = 2 \cdot \color{blue}{5y} \cdot \color{red}{8} $$

We can conclude that the polynomial $ 25y^{2}+80y+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 = 5y } $ and $ \color{red}{ B = 8 } $ so,

$$ 25y^{2}+80y+64 = ( \color{blue}{ 5y } + \color{red}{ 8 } )^2 $$

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