Question

determinati c.m.m.d.c al nr :

a) a=9•3•5²-3³ si b=3³•3²-9²
b) a=16³-16² si b=14²+14³
c) a=(2²•5)³+20² si b=5•(5•7³-3•7²)
d) a=4³+2⁵ si b=4²+2⁷

Answer 1

a)
a=9×3×5²-3³ =3²×3×5²-3³ =3³×5²-3³ =3³(5²-1)=3³×(25-1)=3³×24=3³×2³×3=
=3⁴×2³
b=3³×3²-9²=3⁵-3⁴=3⁴(3-1)=3⁴×2
cmmdc=2×3⁴
b)
a=(2⁴)³-(2⁴)² =2¹²-2⁸×(2⁴-1)= 2⁸×(2⁴-1)=2⁸×15= 2⁸×3×5
b=14²+14³ =14²(1+14)=2²×7²×15=2²×7²×3×5
cmmdc=2²×3×5

c)
a=(2²×5)³+20² =20³+20² =20²(20+1)=2⁶×5²×21=2⁶×5²×3×7
b=5×(5×7³-3×7²)=5×7²×(5×7-3)=5×7²×(35-3)=5×7²×32=5×7²×2⁵
cmmdc=2⁵×5×7

d)
a=4³+2⁵=2⁶+2⁵=2⁵×(2+1)=2⁵×3
b=4²+2⁷ =2⁴+2⁷ =2⁴×(1+2³) =2⁴×9 =2⁴×3²
cmmdc=2⁴×3