x^3z-4x^2yz+4xy^2z
=xz(x^2-4xy+4y^2)
=xz(x-2y)^2
(x+2)(x+3)+3x+1
=x^2+3x+2x+6+3x+1
=x^2+8x+7
=(x+1)(x+7)
x^2-4y^2+x+2y
=(x^2-4y^2)+(x+2y)
=(x+2y)(x-2y)+(x+2y)
=(x+2y)(x-2y+1)
x^2-6x+9-y^2
=(x^2-6x+9)-y^2
=(x-3)^2-y^2
=(x-3+y)(x-3-y)
x^2-x-30
=(x+5)(x-6)
a^2-5a+4
=(a-1)(a-4)
(x+y)^2-14(x+y)+49
=[(x+y)-7]^2
=(x+y-7)^2