GUNÌTA SAMUCCAYAH - SAMUCCAYA GUNÌTAH

In connection with factorization of quadratic expressions a sub-Sutra, viz. 'Gunita samuccayah-Samuccaya Gunitah' is useful.
It is intended for the purpose of verifying the correctness of obtained answers in multiplications, divisions and factorizations.

It means in this context: 'The product of the sum of the coefficients(sc) in the factors is equal to the sum of the coefficients(sc) in the product'

Symbolically we represent as sc of the product = product of the sc (in the factors)/p>

Example 1:     (x + 3) (x + 2) = x2 + 5x + 6
          Now ( x + 3 ) ( x + 2 ) = 4 x 3 = 12 : Thus verified.

Example 2:     (x + 5) (x + 7) (x - 2) = x3 + 10x2 + 11x - 70
          (1 + 5) (1 + 7) (1 - 2) = 1 + 10 + 11 - 70
          i.e.,     6 x 8 x -1 = 22 - 70
          i.e.,     -48 = -48 Verified.

Verify whether the following factorization of the expressions are correct or not by the Vedic check:
i.e. Gunita. Samuccayah-Samuccaya Gunitah:

    1.     (2x + 3) (x - 2) = 2x2 - x - 6
    2.     12x2 - 23xy + 10y2 = ( 3x - 2y ) ( 4x - 5y )
    3.     12x2 + 13x - 4 = ( 3x - 4 ) ( 4x + 1 )
    4.     ( x + 1 ) ( x + 2 ) ( x + 3 ) = x3 + 6x2 + 11x + 6