a.) x2 -6xy+ 9y2 - z2 +2z-1
=(x-3y)2 - (z-1)2
=(x-3y-z+1) (x-3y+z-1)
b) x3 + 3x2 + 4x +12
= x2(x+3) + 4(x+3)
=(x+3)(x2+4)
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\(x^3+3x^2+4x+12\)
\(=x^2\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x^2+4\right)\left(x+3\right)\)
\(x^2-6xy+9y^2-z^2+2z-1\)
\(=x^2-2.x.3y+\left(3y\right)^2-\left(z^2-2z+1\right)\)
\(=\left(x-3y\right)^2-\left(z-1\right)^2\)
\(=\left(x-3y-z+1\right)\left(x-3y+z-1\right)\)
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