Answer
$33x^{2}-80x+7$
Work Step by Step
a)Subtract by combining like terms
$(49x^{2}-56x+16)-(16x^{2}+24x+9)$
..remove parentheses.
$=49x^{2}-56x+16-16x^{2}-24x-9$
...combine like terms.
$=(49x^{2}-16x^{2})+(-56x-24x)+(16-9)$
$=33x^{2}-80x+7$
or
b) Factor each expression and then use the rule for a difference of two squares.
$(49x^{2}-56x+16)-(16x^{2}+24x+9)$
...write each expression as a square of a binomial.
$=(7x-4)^{2}-(4x+3)^{2}$
...use the rule for a difference of two squares.
$=[(7x-4)+(4x+3)][(7x-4)-(4x+3)]$
...remove the inner parentheses and combine like terms.
$=(7x-4+4x+3)(7x-4-4x-3)$
$=(11x-1)(3x-7)$
...multiply the parentheses.
$=33x^{2}-77x-3x+7$
...add like terms.
$=33x^{2}-80x+7$
