a. $7x^{2}$ - 7xy -5x + 5y
= 7x(x-y) -5(x-y)
=(x-y) (7x-5)
b. $x^{2}$ -6x + 9 -$9y^{2}$
= $(x-3)^{2}$ - $(3y)^{2}$
= (x-3-3y)(x-3+3y)
c. 2xy + 3z +6y + xz
=2y(x+3) + z(x+3)
=(x+3)((2y+z)
d. $a^{4}$ + $6a^{2}$ + 9 - $36t^{2}$
= $(a^{2}+ 3)^{2}$ - $(6t)^{2}$
= ($a^{2}$ +3 -6t)($a^{2}$ +3 +6t)
e. $a^{2}$ + 2ab + $b^{2}$ -$x^{2}$ +2xy - $y^{2}$
= $(a+b)^{2}$ - $(x+y)^{2}$
= (a+b-x-y)(a+b+x+y)
g. $x^{2}$ - 4$x^{2}$ $y^{2}$ + $y^{2}$ +2xy
= $(x+y)^{2}$ - $(2xy)^{2}$
= (x+y-2xy)(x+y+2xy)
h.25 -$a^{2}$ + 2ab - $b^{2}$
= -($a^{2}$ - 2ab + $b^{2}$ -25 )
= -($(a-b)^{2}$ -$5^{2}$ )
= -[(a-b-5)(a-b+5)]