Factorization using Vedic Mathematics is done by using 2 Sutras. Combo Rule (Perfect Quadratic Expression): We use combination of 2 sutras. Anurupyena(Proportionality). Adyamadyenantyamantya (1st by 1st and last by last) (explained below): In Anurupyena, we split the middle term (coefficient of x) of quadratic equation in 2 terms such that Proportion/Ratio of coeff of x2 term to 1st coeff of x term = Ratio of 2nd coeff of x term to constant term. That ratio of the 1st 2 coeff is one of the root of equation. Adyamadyenantyamantya In Adyamadyenantyamantya (Commonly called as Adyamadyena), we divide the first term’s coeff of eq with 1st term of factor obtained above and last term of eq with the last term of the same factor. Sanskrit Name (For Adyamadyenantyamantya): आद्यमाद्ये नान्त्यमन्त्येन English Translation (For Adyamadyenantyamantya): 1st by 1st and last by last Examples: 2x2 + 5x -3 Anurupyena: Split middle terms coeff(5) in 2 parts such that coeff of x2 term to 1st coeff of x term = Ratio of 2nd coeff of x term to constant term.Hence split it in 6 and -1 (2/6 = -1/-3) => 2x2 + 6x –x -3So 1st factor: x+3 (2:6) Adyamadyenantyamantya: Divide the first term’s coeff (2) of eq by 1st term of factor(1) and divide last term of eq (-3) by 2st term of factor (3)So 2nd factor: 2x-1   Similarly, 4x2 + 12x + 5 = (2x+1)(2x+5) 9x2 -15x + 4 = (3x-1)(3x-4) 6x2 + 11x -10 = (2x+5)(3x-2) Here we come across to another important sutra Gunitasamuccaya Samuccayagunita Gunitasamuccaya Samuccayagunita Sanskrit Name: गुणितसमुच्चयः समुच्चयगुणितः Commonly called as Gunitasamuccaya. English Translation: Product of the sum of the coefficients of the factors = sum of the coefficients in the product. Example: 4x2 + 12x + 5 = (2x+1)(2x+5) Sum of the coefficients in the product: 4 + 12 + 5 =21 Product of the sum of the coefficients of the factors: (2+1)(2+5) = 21   Lopana Sthapanabhyam (Subsutra of … [Read more...]