C, \(x^2+2xy+y^2-x-y-12\)
\(=\left(x+y\right)^2-\left(x+y\right)-12\)
\(=\left(x+y\right)^2-4\left(x+y\right)+3\left(x+y\right)-12\)
\(=\left(x+y\right)\left(x+y-4\right)+3\left(x+y-4\right)\)
\(=\left(x+y-4\right)\left(x+y+3\right)\)
a) (x^2-3)^2+16
=(x4-2.x2.3+32)+16
=(x4-6x2+9)+16
=x4-6x2+9+16
=x4-6x2+25
b)(x^2-x)^2-2(x^2+x)-15
=(x4-2x3+x2)-(2x2-2x)-15
=x4-2x3+x2-2x2+2x-15
=x4-2x3-x2+2x-15
=(x4-2x3)-(x2-2x)-15
=x3(x-2)-x(x-2)-15
=(x-2)(x3-x)-15