Factor polynomial $$ 9r^{2}-12r+4 $$
Answer
$$ 9r^{2}-12r+4 = ( 3r-2 )^{ 2 } $$
Explanation
Both the first and third terms are perfect squares.
$$ 9x^2 = \left( \color{blue}{ 3r } \right)^2 ~~ \text{and} ~~ 4 = \left( \color{red}{ 2 } \right)^2 $$The middle term ( $ -12x $ ) is two times the product of the terms that are squared.
$$ -12x = - 2 \cdot \color{blue}{3r} \cdot \color{red}{2} $$We can conclude that the polynomial $ 9r^{2}-12r+4 $ 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 = 3r } $ and $ \color{red}{ B = 2 } $ so,
$$ 9r^{2}-12r+4 = ( \color{blue}{ 3r } - \color{red}{ 2 } )^2 $$This page was created using
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