Factor polynomial $$ 64x^{2}+112x+49 $$
Answer
$$ 64x^{2}+112x+49 = ( 8x+7 )^{ 2 } $$
Explanation
Both the first and third terms are perfect squares.
$$ 64x^2 = \left( \color{blue}{ 8x } \right)^2 ~~ \text{and} ~~ 49 = \left( \color{red}{ 7 } \right)^2 $$The middle term ( $ 112x $ ) is two times the product of the terms that are squared.
$$ 112x = 2 \cdot \color{blue}{8x} \cdot \color{red}{7} $$We can conclude that the polynomial $ 64x^{2}+112x+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 = 8x } $ and $ \color{red}{ B = 7 } $ so,
$$ 64x^{2}+112x+49 = ( \color{blue}{ 8x } + \color{red}{ 7 } )^2 $$This page was created using
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