Answer
$b=30$ or $b=-30$
Work Step by Step
RECALL:
There are two forms of perfect square trinomials:
(1) $m^2+2mn+n^2$, which is the square of $(m+n)^2$; and
(2) $m^2-2mn+n^2$, which is the square of $(m-n)^2$
The given trinomial has:
$m^2 = 9p^2=(3p)^2$, which means that $m=3p$
$n^2=25=5^2$, which means that $n=5$
Thus, the given trinomial will be a perfect square if
(i) $bp=2mn=2(3p)(5) = 30p$, which means that $b=30$; and when
(ii) $bp=-2mn=-2(3p)(5) = -30p$, which means that $b=-30$
Therefore, the given polynomial is a perfect square when $b=30$ and when $b=-30$
