Gunakasamuchyah

“It means the product of the sum of the coefficients in the factors is equal to the sum of the coefficients in the product”. In symbols we may put this principle as follows:
Sc of the product = product of the Sc (in factors).
For example: (x + 7) (x + 9) = x² + 16 x + 63 and we observe (1 + 7) (1 + 9) = 1 + 16 + 63 = 80. Similarly in the case of cubics, biquadratics etc. the same rule holds good. For example (x + 1) (x + 2) (x + 3) = x³ + 6x² + 11 x + 6 2 × 3 × 4 = 1 + 6 + 11 + 6 = 24.
Thus, if and when some factors are known this rule helps us to fill in the gaps.
It will be found useful in the factorization of cubics, biquadratics and will also be discussed in some other such contexts later on.