Gunitasamuchyah
The product of the sum is equal to the sum of the products (gu · ni · ta · sa · mu · cha · yah)
What it means
A polynomial factor-check. After you factor an expression, plug x = 1 into both the original AND the factored form. If both give the same number, the factoring is correct. If they differ, there's an error — and you found it without multiplying the factors back out.
Worked example
Is (x + 3)(x + 4) the correct factoring of x² + 7x + 12? Plug in x = 1. Factored form: (1+3)(1+4) = 4 × 5 = 20. Original: 1 + 7 + 12 = 20. They match — factoring is correct.