#### Answer

$a.\quad x^{2}-81$
$b.\quad 36-m^{4}$
$c.\quad 9c^{2}-16$

#### Work Step by Step

a. $(x+9)(x-9)$
...identify which terms correspond to $a $ and $b $ in the rule for the product of a sum and difference.$(a+b)(a-b)=a^{2}-b^{2}$)
$a=x,\ b=9$
...substitute for $a $ and $b $ in the rule
$(x+9$)$(x-9)=x^{2}-9^{2}$
...simplify.
$=x^{2}-81$
b. $(6+m^{2})(6-m^{2})$
...identify which terms correspond to $a $ and $b $ in the rule for the product of a sum and difference.$(a+b)(a-b)=(a^{2}-b^{2}$)
$a=6,\ b=m^{2}$
...substitute for $a $ and $b $ in the rule
$(6+m^{2})(6-m^{2})=6^{2}-(m^{2})^{2}$
...simplify.
$=36-m^{4}$
c. $(3c-4)(3c+4)$
...identify which terms correspond to $a $ and $b $ in the rule for the product of a sum and difference.($(a+b)(a-b)=a^{2}-b^{2}$)
$a=3c,\ b=4$
...substitute for $a $and $b $in the rule
$(3c-4)(3c+4)=(3c)^{2}-4^{2}$
...simplify.
$=9c^{2}-16$