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P^2 + 14p + 49 is a perfect square trinomial. Justify your answer

P^2 + 14p + 49 is a perfect square trinomial. Justify your answer
asked 13.6k views
4 votes
P^2 + 14p + 49 is a perfect square trinomial. Justify your answer

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User Dylan Smith
by
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2 Answers

3 votes

\bf \begin{array}{cccccllllll} {{ a}}^2& + &2{{ a}}{{ b}}&+&{{ b}}^2\\ \downarrow && &&\downarrow \\ {{ a}}&& &&{{ b}}\\ &\to &({{ a}} + {{ b}})^2&\leftarrow \end{array}\qquad \qquad \qquad \begin{array}{cccccllllll} {{ a}}^2& - &2{{ a}}{{ b}}&+&{{ b}}^2\\ \downarrow && &&\downarrow \\ {{ a}}&& &&{{ b}}\\ &\to &({{ a}} - {{ b}})^2&\leftarrow \end{array}\\\\ -------------------------------


\bf \begin{array}{llll} p^2+14p+49\\\\ p^2+2(p)(7)+7^2 \end{array} \qquad \implies\qquad \begin{array}{cccccllllll} {{ p}}^2& + &2{{ (p)}}{{ (7)}}&+&{{ 7}}^2\\ \downarrow && &&\downarrow \\ {{ p}}&& &&{{ 7}}\\ &\to &({{ p}} + {{ 7}})^2&\leftarrow \end{array}
answered
User Li
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7.9k points
6 votes
it factors as (p + ,7)² so there ya go
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User Bhavani Ravi
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8.6k points
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