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

$24x^{2}+58x-65$
a) (without factoring) Subtract by combining like terms $(25x^{2}+40x+16)-(x^{2}-18x+81)$ ..remove parentheses. $=25x^{2}+40x+16-x^{2}+18x-81$ ...combine like terms. $=(25x^{2}-x^{2})+(40x+18x)+(16-81)$ $=24x^{2}+58x-65$ b) Factor each expression and then use the rule for a difference of two squares. $(25x^{2}+40x+16)-(x^{2}-18x+81)$ ...write each expression as a square of a binomial. $=(5x+4)^{2}-(x-9)^{2}$ ...use the rule for a difference of two squares. $=[(5x+4)+(x-9)][(5x+4)-(x-9)]$ ...remove the inner parentheses and combine like terms. $=(5x+4+x-9)(5x+4-x+9)$ $=(6x-5)(4x+13)$ ...multiply the parentheses. $=24x^{2}+78x-20x-65$ ...add like terms. $=24x^{2}+58x-65$