Factor polynomial $$ 9x^{2}+42x+49 $$
Answer
$$ 9x^{2}+42x+49 = ( 3x+7 )^{ 2 } $$
Explanation
Both the first and third terms are perfect squares.
$$ 9x^2 = \left( \color{blue}{ 3x } \right)^2 ~~ \text{and} ~~ 49 = \left( \color{red}{ 7 } \right)^2 $$The middle term ( $ 42x $ ) is two times the product of the terms that are squared.
$$ 42x = 2 \cdot \color{blue}{3x} \cdot \color{red}{7} $$We can conclude that the polynomial $ 9x^{2}+42x+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 = 3x } $ and $ \color{red}{ B = 7 } $ so,
$$ 9x^{2}+42x+49 = ( \color{blue}{ 3x } + \color{red}{ 7 } )^2 $$This page was created using
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