Answer
$24x^{2}+58x-65$
Work Step by Step
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.
$=24x^{2}+58x-65$
