#### Answer

$(3p-7)^{2}$

#### Work Step by Step

$9p^{2}-42p+49=$
...write first and last terms as squares.
$=(3p)^{2}-42p+(7)^{2}$
...does middle term equal $2ab$?
$-42p=-2\cdot(3p)\cdot(7)$
yes.
$=(3p)^{2}-2\cdot(3p)\cdot(7)+(7)^{2}$
...write as the square of a binomial.
$=(3p-7)^{2}$