a, $5xy^{2}$ - 10xyz + $5xz^{2}$
= 5x.($y^{2}$ - 2yz + $z^{2}$ )
= 5x .($x-z)^{2}$
b, x(x+y) - 2x - 2y
= x.(x+y) - (2x+2y)
= x.(x+y) - 2.(x+y)
= (x+y).(x-2)
d, $x^{4}$ + $4x^{3}$ - $x^{2}$$y^{2}$ + $4x^{2}$
= $x^{2}$($x^{2}$ - 4x- $y^{2}$ + 4)
= $x^{2}$ [($x-2)^{2}$ - $y^{2}$]
= $x^{2}$ .(x-2-y).(x-2+y)
e, 2xy + $z^{2}$ - $x^{2}$ - $y^{2}$
= ($-x-y)^{2}$ + $z^{2}$
= -($x+y)^{2}$ + $z^{2}$
= -(x+y+z)(x+y-z)
g, 4xy - $x^{2}$ + 25 - $4y^{2}$
= 4xy - $x^{2}$ + $5^{2}$ - $4y^{2}$
= $5^{2}$ - [$x^{2}$ + 5xy - ($2y)^{2}$]
= $5^{2}$ - $(x-2y)^{2}$
= (5-x+2y)(5+x-2y)