Finding HCF of expressions using Vedic Mathematics Highest Common Factor (HCF) as the name suggests it is the highest common factor present between 2 or more expressions or numbers For Example: HCF of 8 and 10 is 2. While that of 8 and 12 is 4 and so on. In this topic we are going to see the HCF of expressions. Calculation of HCF can be done in following ways: Adyamadyena Rule to find the factors of the expression and name the common factor/s as the HCF. Lopanasthapana Method by elimination and retention method or Sankalana-Vyavakalana Process which means addition and subtraction to eliminate and retain the highest power of dependent term. We will be using 2nd way. Examples: Find HCF of x2 + 7x + 6 and x2 -5x -6 So HCF = x+1 Find HCF of 4x3 + 13x2 + 19x + 4 and 2x3 + 5x2 + 5x -4 While subtraction we multiplied eq 2 by 2 and done subtracted from eq1 for elimination x3 term. So HCF = x2+ 3x + 4 Find HCF of x4+ x3 -5x2– 3x+2 and x4-3x3+x2+3x-2 So HCF = x2-x-2 … [Read more...]
Factorization using Vedic Mathematics
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...]
(cont.) Equattions 3
Paravartya As seen before Paravartya Sutra of Vedic Mathematics means 'Transpose and Apply'. Prerequisites: Equation should be in following manner. As can be seen Numerator is obtained by addition of each term multiplied by absent term with sign reversed(Transpose). Examples: Sopantyadvavyamantyam Sanskrit Name: सोपान्त्यद्वयमन्त्यं English Translation: The Ultimate and twice the penultimate. Meaning: If Equations are in the below form then 2C(penultimate) + D(ultimate) = 0 Examples: Antyayoreva Sanskrit Name: अन्त्ययोरेव Meaning It has different meaning in different context. Contexts Context1 Equations present in following manner Examples: Context2 Meaning: Sum of the series is a fraction whose numerator is sum of the numerators in the series and whose denominator is the product of the 2 ends i.e. 1st and last binomials. Equations present in following manner Examples: Context3 This type is very similar to that of Conext2 only difference in the numerator of each term. Numerator is equal to difference between the binomial factors of its denominator. … [Read more...]
Division of Polynomials using Vedic Mathematics
Division of Polynomials/Expressions Using Paravartya Sutra in Vedic Mathematics To divide polynomials we use the concept of Paravartya (Transpose and Apply). We are very much familiar with these types. This as in today are very similar to Synthetic Division/Honer’s Method. Examples: For 1st example, For Dividend part, take only coefficients. Divisor is x-2 i.e. 1x - 2. Like Paravartya Sutra, ignore 1st digit i.e. 1 and take transpose of -2 which is 2. Now, Carry on as Paravartya Sutra. … [Read more...]
Vedic Mathematics
Vedic Mathematics is highly fast, simple & effective tool for carrying out basic arithmetics like subtraction, multiplication, division, squaring, cubing, finding square roots & cube roots, etc. Vedic Mathematics techniques can be divided in 2 basic techniques – General and Specific techniques. General method can be applied to any set of numbers whereas Specific method can be applied to specific numbers depending on their face value or position of each number. So it is very important to know both general and specific techniques to use Vedic Mathematics effectively. [slideshow gallery_id="1" showthumbs=true thumbsposition=top thumbsborder=#00ffCC] Replacing our Regular (Usual) school taught techniques with Vedic Mathematics is never going to be possible but for mental calculations & for those exams where one cannot afford to spend much time, I feel these techniques should be known and practiced on regular basis. The name ‘Vedic Mathematics’ will make someone to assume that this branch of mathematics have some relations with Vedas but many Indian scholars have proved that it has no roots from Vedas and since then the name ‘Vedic Mathematics’ have been contradictory. But the techniques used in it are genuinely effective when it comes to doing Math mentally or on paper in lesser steps. But even after knowing the power of techniques, Vedic Mathematics, sadly and surprisingly, is hardly taught in schools and colleges. … [Read more...]
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