1,
a, =(x+2)^2-y^2
=(x+2+y)(x+2-y)
b, =3(x^2+2xy+y^2-z^2)
=3((x+y)^2)-z^2)
=3(z-y-x)(z+y+x)
c, =(x^3+x^2)+(x^2+x)+(x+1)
=x^2(x+1)+x(x+1)+(x+1)
=(x^2+x+1)(x+1)
d, =x^3-3x^2-x^2+3x+9x-27
=x^2(x-3)-x(x-3)+9(x-3)
=(x^2-x+9)(x-3)
e, =(x^2-4y^2)-(2x+4y)
=(x-2y)(x+2y)-2(x+2y)
=(x+2y)(x^2+2x+2)
f, =x^4−2x^2+2x^3−4x+2x^2−4
=x^4-2x^2+2x^3-4x+2x^2-4
=x^2(x^2−2)+2x(x^2−2)+2(x^2−2)
=x^2(x^2-2)+2x(x^2-2)+2(x^2-2)
=(x^2−2)(x^2+2x+2)
g, =-(x^2-x+2)(x^2+x+2)
h, =x^3+3x^2y+x+3xy^2+y+y3x^3+3x^2y+x+3xy^2+y+y^3
=(x^3+3x^2y+3xy^2+y^3)+(x+y)
=(x^3+3x^2y+3xy^2+y^3)+(x+y)
=(x+y)^3+(x+y)
=(x+y)^3+(x+y)
=(x+y)[(x+y)^2+1]
=(x+y)[(x+y)^2+1]
=(x+y)(x^2+y^2+2xy+1)
=(x+y)(x^2+y^2+2xy+1)
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