Algebraic Multiplication using Vedic Maths

Lets example to understand this method(x + 3) (3x + 4)

Step I

Write one binomial under the other binomial as shown underx + 33x + 4 Multiply the digits on right side column vertically3× 4 = 12

Step 2

x + 33x + 4

Now multiply cross wise and add. Shown as under(x × 4) + (3x × 3)

4x + 9x = 13x

Step 3

x + 33x + 4

Now vertically multiply on left hand side columnx × 3x = 3x2

So, The answer is = 3x2 + 13x + 12

Two Trinomials using (3 × 3)

Lets another example to understand it

(2x2 + x + 5) (3x2 + 2x + 6)

Step 1

Write one trinomial under the other as shown below

2x2 + x + 5

3x2 + 2x + 6

On left hand side column , multiply vertically

2x2 × 3x2 = 6x4

Step 2

Now Cross wise multiplication with first two columns

2x2 + x + 5

3x2 + 2x + 6

= (2x2 × 2x) + (3x2 × x)

= 4x3 + 3x3

= 7x3

Step 3

Now multiply cross wise extreme left and extreme right columns

Multiply Middle Column vertically

And add the all three products. As shown below

2x2 + x + 5

3x2 + 2x + 6

= (2x2 × 6) + (3x2 × 5) + ( x × 2x)

= 12x2 + 15x2 + 2x2

= 29x2

Step 4

Now multiply cross wise middle column with extreme last column (right side)

2x2 + x + 5

3x2 + 2x + 6

= (2x × 5) + (x × 6)

10x + 6x

= 16x

Step 5

Right Hand side Vertically Multiplication

2x2 + x + 5

3x2 + 2x + 6

= 5 × 6

= 30

Answer = 6x4 + 7x3 + 29x2 + 16x + 30

Practise it: vertically and crosswise works the same way on plain numbers, so try it in our multiplication game.