242 Involution of Polynomials. 
Ex. 3. Find the coefficients of LS it 
Here P=5 X4X3X2X1= 120 
P 
z= - - - 60} a2bed 
aa . - - 30] abc 
2 
eae - - 20| a%be 
er se 
| 539- - ee - 10: shag 
ee ee ee 
s : | 
i 
_ Hence pidbacde wa-45a'b+ 100%%? + 20a°be 30a*b*c 
+604? bed +120abcde+&e 
If the number of terms in the root is caine than the index of 
the power, the excess produces no change in the coefficients, as 
no more than 7 letters can enter any term of the power, é 
Ez. A. Find the coefficients of a+b+c+d’°, 
_ The binomial coefficients are 1, 6, 15, 20.. The introduction 
of the third term c, gives us 2A=30, 3B=60. And the fourth 
term d, gives 2°3B= 120, 3-4C=180. 
Hence a+b+e+d°=a*+6a°b+ 15a‘h? + 20a3b* + 30a*be 
+60a*b?2c+120a* bed+ 1800°b2cd+&c. 
Or we might have found P as before, Gbserving that as two 
terms are deficient in the root, P must have at least two divisions 
before the consequent coefficient can enter into the expression of 
the power. 
P=6x5x*4X3 x2 720 sess 
P 
* tex - - - 360 a? bede 
er? ; 
2, eee - ~ 180| a2b?cd 
ee ear ~ 120] a%bed 
P 3 i 
22-3 - = °°601 @3b2e 
PEE al RAAB Ae a Ce dow Lake tale 2 ee SNe Lies 
