a)
x3−3x2+2=x3−x2−2x2+2=x2(x−1)−2(x2−1)=(x−1)x2−2(x+1)(x−1)=(x−1)x2−(2x+2)(x−1)=(x−1)(x2−2x−2)
b)
a7+a2+1=a7−a+a2+a+1=a(a6−1)+a2+a+1=a(a3+1)(a3−1)+a2+a+1=(a4+a)(a−1)(a2+a+1)+a2+a+1=(a5−a4+a2−a)(a2+a+1)+a2+a+1=(a2+a+1)(a5−a4+a2−a+1)
c)
4x2−25+(2x+7)(5−2x)=(2x−5)(2x+5)−(2x+7)(2x−5)=(2x−5)(2x+5−2x−7)=−2(2x−5)
d)
x3−2y3−3xy2=x3−xy2−2xy2−2y3=x(x2−y2)−2y2(x+y)=x(x−y)(x+y)−2y2(x+y)=(x2−xy)(x+y)−2y2(x+y)=(x+y)(x2−xy−2y2)=(x+y)(x2−y2−xy−y2)=(x+y)[(x−y)(x+y)−y(x+y)]=(x+y)(x+y)(x−y−y)=(x+y)2(x−2y)
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