Question
Factor polynomial $$ 144f^{2}-24f+1 $$
Answer
$$ 144f^{2}-24f+1 = ( 12f-1 )^{ 2 } $$
Explanation
Both the first and third terms are perfect squares.
$$ 144x^2 = \left( \color{blue}{ 12f } \right)^2 ~~ \text{and} ~~ 1 = \left( \color{red}{ 1 } \right)^2 $$The middle term ( $ -24x $ ) is two times the product of the terms that are squared.
$$ -24x = - 2 \cdot \color{blue}{12f} \cdot \color{red}{1} $$We can conclude that the polynomial $ 144f^{2}-24f+1 $ 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 = 12f } $ and $ \color{red}{ B = 1 } $ so,
$$ 144f^{2}-24f+1 = ( \color{blue}{ 12f } - \color{red}{ 1 } )^2 $$This page was created using
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