Sopaantyadvayamantyam- "The ultimate and twice the penultimate"

Corollary : Gunitasamuccayah Samuccayagunitah -"The product of the sum of the coefficients in the factors is equal to the sum of the coefficients in the product"

 

S_c of the product = Product of the S_c in the factors

For example (x+7) (x+9) = (x² + 16x + 63)

(1+7) (1+9) = (1 + 16 + 63) = 80

or (x+1) (x+2) (x+3) = (x³ + 6X² + 11x + 6)

(1+1) (1+2) (1+3) = (1 + 6 + 11 + 6) = 24