$a)_{}$ $(x-5)^2-16_{}$
$=(x-5)^2-4^2_{}$
$=(x-5-4)(x-5+4)_{}$
$=(x-9)(x-1)_{}$
$b)_{}$ $25-(3-x)^2_{}$
$=5^2-(3-x)^2_{}$
$=(5-3-x)(5+3-x)_{}$
$=(2-x)(8-x)_{}$
$c)_{}$ $(7x-4)^2-(2x+1)^2_{}$
$=[ 7x-4-(2x+1)].[ 7x-4+(2x+1)]_{}$
$=(7x-4-2x-1)(7x-4+2x+1)_{}$
$=(5x-5)(9x-3)_{}$
$=5.(x-1).3.(3x-1)_{}$
$=15.(x-1)(3x-1)_{}$
$d)_{}$ $49.(y-4)^2-9.(y+2)^2_{}$
$=[ 7.(y-4)-4.(y+2)].[ 7.(y-4)+3.(y+2)]_{}$
$=(7y-28-3y-6)(7y-28+3y+6)_{}$
$=(4y-34)(10y-22)_{}$
$=2.(2y-17).2.(5y-11)_{}$
$=4.(2y-17)(5y-11)_{}$
$e)_{}$ $x^{16}+1$
$=(x^8-1)(x^8+1)_{}$
$=(x^4-1)(x^4+1)(x^8+1)_{}$
$=(x^2-1)(x^2+1)(x^4+1)(x^8+1)_{}$
$=(x-1)(x+1)(x^2+1)(x^4+1)(x^8+1)_{}$
$f)_{}$ $x^2-6x-y^2+9_{}$
$=(x-3)^2-y^2_{}$
$=(x-3-y)(x-3+y)_{}$
