## Algebra 1: Common Core (15th Edition)

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