Factor polynomial $$ 10g^{2}+100g+250 $$

$$ 10g^{2}+100g+250 = 10( g+5 )^{ 2 } $$

Step 1 :

After factoring out $ 10 $ we have:

$$ 10g^{2}+100g+250 = 10 ( g^{2}+10g+25 ) $$

Step 2 :

Both the first and third terms are perfect squares.

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

The middle term ( $ 10x $ ) is two times the product of the terms that are squared.

$$ 10x = 2 \cdot \color{blue}{g} \cdot \color{red}{5} $$

We can conclude that the polynomial $ g^{2}+10g+25 $ 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 = g } $ and $ \color{red}{ B = 5 } $ so,

$$ g^{2}+10g+25 = ( \color{blue}{ g } + \color{red}{ 5 } )^2 $$

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