#### Answer

$4p^{4}-49q^{2}$

#### Work Step by Step

$(2p^{2}+7q)(2p^{2}+7q)$
...identify which terms correspond to $a $ and $b $
in the rule for the product of a sum and difference ($(a+b)(a-b)=a^{2}-b^{2}$).
$a=2p^{2},\ b=7q$
...substitute for $a $and $b $ in the rule
$(2p^{2}+7q)(2p^{2}+7q)=(2p^{2})^{2}-(7q)^{2}$
...simplify.
=$4p^{4}-49q^{2}$