"The factors of the sum are equal to the sum of the factors."
11(9+4) → 11×13 = 143. Add inside, multiply outside!
Distributing a multiplier over a sum using the distributive property for faster mental calculation.
Multiply a number by a sum by first computing the sum inside the bracket, then multiplying by the outer factor.
This sutra is the complement of Gunitasamuccayah. While the previous sutra says "product of sums = sum of products", this one says "factors of the sum = sum of the factors." In practice, when you see a×(b+c), you first compute b+c, then multiply by a. This is often faster than computing a×b + a×c separately. Example: 25 × (4+8) = 25 × 12 = 300, which is easier than 25×4 + 25×8 = 100+200 = 300. The sutra also applies to factoring verification: if the product of a polynomial's factor sums equals the sum of the polynomial's coefficients, the factoring is correct.
This sutra completes the duality of the 15th sutra and together they represent the full power of the distributive law in Vedic Mathematics. Bharati Krishna Tirtha placed great emphasis on these twin sutras as they bridge arithmetic and algebra. The technique of "sum then multiply" versus "multiply then sum" reflects the ancient Indian philosophical concept of "upaya" (skillful means) — choosing the easier path to the same result. In the Kerala School tradition, Nilakantha Somayaji (1444–1544 CE) used similar algebraic transformations in his astronomical calculations.
This is the distributive law a(b+c) = ab + ac read in reverse: compute the sum first (b+c), then multiply by a. In computational complexity, choosing the order of operations can significantly affect efficiency — matrix multiplication, for instance, can vary from O(n²) to O(n³) depending on the order. In numerical analysis, summing before multiplying often reduces floating-point errors due to catastrophic cancellation. This sutra also underpins the factoring verification technique: evaluating P(1) gives the sum of coefficients, and should equal the product of factor sums.