Factor polynomial $$ 49p^{8}+42p^{4}+9 $$
Answer
$$ 49p^{8}+42p^{4}+9 = ( 7p^{4}+3 )^{ 2 } $$
Explanation
Both the first and third terms are perfect squares.
$$ 49x^8 = \left( \color{blue}{ 7p^{4} } \right)^2 ~~ \text{and} ~~ 9 = \left( \color{red}{ 3 } \right)^2 $$The middle term ( $ 42x^4 $ ) is two times the product of the terms that are squared.
$$ 42x^4 = 2 \cdot \color{blue}{7p^{4}} \cdot \color{red}{3} $$We can conclude that the polynomial $ 49p^{8}+42p^{4}+9 $ 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 = 7p^{4} } $ and $ \color{red}{ B = 3 } $ so,
$$ 49p^{8}+42p^{4}+9 = ( \color{blue}{ 7p^{4} } + \color{red}{ 3 } )^2 $$This page was created using
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