Question
Factor polynomial $$ 25x^{2}-70x+49 $$
Answer
$$ 25x^{2}-70x+49 = ( 5x-7 )^{ 2 } $$
Explanation
Both the first and third terms are perfect squares.
$$ 25x^2 = \left( \color{blue}{ 5x } \right)^2 ~~ \text{and} ~~ 49 = \left( \color{red}{ 7 } \right)^2 $$The middle term ( $ -70x $ ) is two times the product of the terms that are squared.
$$ -70x = - 2 \cdot \color{blue}{5x} \cdot \color{red}{7} $$We can conclude that the polynomial $ 25x^{2}-70x+49 $ 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 = 5x } $ and $ \color{red}{ B = 7 } $ so,
$$ 25x^{2}-70x+49 = ( \color{blue}{ 5x } - \color{red}{ 7 } )^2 $$This page was created using
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