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a) 4x⁴y²-6x³+8x²y⁴=
m.d.c.(4,6,8)=2
m.d.c.(x⁴,x³,x²)=x²
m.d.c.(y⁴,y³,y²)=y²
b) 18ab³c²+27a³b⁴c³-9a²b⁵c⁴-45a²b³c²
m.d.c.(18,27,9.45)=9
m.d.c.(a³,a²,a)=a
m.d.c.(b⁵,b⁴,b³)=b³
m.d.c.(c⁴,c³,c²)=c²
c) a.(a+3b)-2c.(a+3b)=
(a-2c).(a+3b)
d) x².(x-3y²)-2y.(x-3y²)=
(x²-2y).(x-3y²)
e) (x²+z)+xy.(x²+z)-z.(x²+z)=
(x²+z).(1+xy-z)
f) a⁴b⁶-9c²=
√(a⁴b⁶)=a²b³
√(9c²)3c
(a²b³+3c).(a²b³3c
g) 9a⁴-b⁴
√(9a⁴)=3a²
√(b⁴=b²
(3a²+b²).(3a²-b²
h) 25x⁶+10x³y+y²=
√(25x⁶)=5x³
√(y²)=y
(5x³+y).(5x³+y)
i) 49x⁴+14x²+1=
√(49x4)=7x²
√(1)=1
(7x²+1).(7x2+1)
j) 20a²b²-2a⁴-50b⁴=
-2.(-10a²b²+a4+25b⁴)=
-2.(a⁴-10a²b²+25b⁴)=
√(a⁴)=a²
√(25b⁴)=5b²
-2.(a²+5b²).(a²+5b²)
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