a)
5$x^{2}$ -10xy +5$y^{2}$ -20$z^{2}$
= 5($x^{2}$ -2xy +$y^{2}$ -4$z^{2}$ )
= 5[($x^{2}$ -2xy +$y^{2}$ ) -$(2z)^{2}$ ]
= 5[$(x-y)^{2}$ - $(2z)^{2}$ ]
= 5(x-y+2z)(x-y-2z)
b) $x^{2}$ -$z^{2}$ +$y^{2}$ -2xy
= ($x^{2}$ -2xy+$y^{2}$ ) -$z^{2}$
= $(x-y)^{2}$ -$z^{2}$
= (x-y+z)(x-y-z)
c) $a^{3}$ -ay -$a^{2}$x +xy
= ( $a^{3}$- $a^{2}$x ) - (ay -xy)
= $a^{2}$(a-x) -y(a-x)
= ($a^{2}$ -y)(a-x)
d) $x^{2}$ -2xy -$4z^{2}$ + $y^{2}$
= ( $x^{2}$ -2xy + $y^{2}$ ) -$4z^{2}$
= $(x-y)^{2}$ -$(2z)^{2}$
= (x-y-2z)(x-y+2z)
e) $3x^{2}$ -6xy +$3y^{2}$ -12$z^{2}$
= 3($x^{2}$ -2xy +$y^{2}$ -4$z^{2}$ )
= 3[($x^{2}$ -2xy +$y^{2}$ ) -$(2z)^{2}$ ]
= 3[$(x-y)^{2}$ - $(2z)^{2}$ ]
= 3(x-y+2z)(x-y-2z)
f) $x^{2}$ -6xy -$25z^{2}$ +$9y^{2}$
= $x^{2}$ -6xy +$(3y)^{2}$ -$25z^{2}$
= [ $x^{2}$ -6xy +$(3y)^{2}$ ] -$25z^{2}$
= $(x-3y)^{2}$ - $(5z)^{2}$
= (x-3y-5z)(x-3y+5z)
