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The fifteenth Sutra Gunakasamuccayah or say All the multipliers means the product of the sum of the coefficients in the factors is equal to the sum of the coefficients in the product

i.e ;  Sc of the product = Product of the Sc
This sutra is useful in verifying the correctness of the obtained answers in multiplication , division and factorization .

Example 1:
(x + 5 ) (x + 6) = x2 + 11x +30

Clearly observing the above form , we see that

Sc of the product  = Product of the Sc
        (1+5) (1+6)  =  1 +11 +30
            6 x 7        =   1+ 41
              42          =     42    Hence Verified

This rule holds true for all the cases of cubics , biquadratics, etc

Example 2 :
(x+1) (x+2) (x+5)   =   x 3+ 8x2+ 17 x+10
(1+1) (1+2) (1+5)  =  1+ 8+ 17 +10
2 x 3 x 6               =   9 + 27
36                        =   36    Hence Verified

Thus if and when some factors are known  this rule helps us to fill in the gaps .This is simple but very absolute and effective process .



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