a) x2−4+(x−2)2x2−4+(x−2)2
=(x2−22)+(x−2)2=(x2−22)+(x−2)2
=(x−2)(x+2)+(x−2)2=(x−2)(x+2)+(x−2)2
=(x−2)[(x+2)+(x−2)]=(x−2)[(x+2)+(x−2)]
=(x−2)(x+2+x−2)=(x−2)(x+2+x−2)
=(x−2)(2x)=(x−2)(2x)
=2x(x−2)=2x(x−2)
b) x3−2x2+x−xy2x3−2x2+x−xy2
=x(x2−2x+1−y2)=x(x2−2x+1−y2)
=x[(x−1)2−y2]=x[(x−1)2−y2]
=x(x−1−y)(x−1+y)=x(x−1−y)(x−1+y)
c) x3−4x2−12x+27x3−4x2−12x+27
=(x3+27)−(4x2+12x)=(x3+27)−(4x2+12x)
=(x+3)(x2−3x+9)−4x(x+3)=(x+3)(x2−3x+9)−4x(x+3)
=(x+3)(x2−3x+9−4x)=(x+3)(x2−3x+9−4x)
=(x+3)(x2−7x+9)