Factor polynomial $$ 25a^{2}+60a+36 $$
Answer
$$ 25a^{2}+60a+36 = ( 5a+6 )^{ 2 } $$
Explanation
Both the first and third terms are perfect squares.
$$ 25x^2 = \left( \color{blue}{ 5a } \right)^2 ~~ \text{and} ~~ 36 = \left( \color{red}{ 6 } \right)^2 $$The middle term ( $ 60x $ ) is two times the product of the terms that are squared.
$$ 60x = 2 \cdot \color{blue}{5a} \cdot \color{red}{6} $$We can conclude that the polynomial $ 25a^{2}+60a+36 $ 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 = 5a } $ and $ \color{red}{ B = 6 } $ so,
$$ 25a^{2}+60a+36 = ( \color{blue}{ 5a } + \color{red}{ 6 } )^2 $$This page was created using
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