Algebraic Multiplication using Vedic Maths

Today we will learn about Algebraic Multiplication in simple and easiest way. Lets know the easiest and small steps way for solving algebraic multiplication by Vedic Method. 

Conventional Method

CASE I (Simple Case)[Two Trinomials using (2 × 2)]

(x+ 5) (4x - 7)
x(4x-7) + 5(4x-7)

[x × 4x + x × (-7)] + [5 × 4x + 5 × (-7)]
4x² - 7x + 20x -35
4x²- 13x - 35(It is very complicated method and always a chance of error vests in it) Now we will apply Vedic Method. Vedic Method is easy and simple 

Vedic Maths Method

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

CASE II [Two Trinomials using (3 × 3)]

[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

CASE III [If power of x is absent]

Always take zero (0) as coefficient and then solve the question exactly as before. Lets take an example
(x² + 3x + 5) (2x² + 8)

Step I
On left hand side column , multiply vertically
x² + 3x + 5
2x² + 0x+ 8

= x² ×  2x²
= 2x⁴

Step 2
Now Cross wise multiplication with first two columns
x² + 3x + 5
2x² + 0x+ 8

= (x² × 0x)  + (2x² × 3x)
= 0 +  6x²
=  6x³

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

x² + 3x + 5
2x² + 0x+ 8

= (x² × 8)  + (2x² × 5) + ( 3x × 0x)
= 8x² + 10x² + 0
= 18x²


Step 4
Now multiply cross wise middle column with extreme last column
x² + 3x + 5
2x² + 0x+ 8
= (3x × 8)  + (0x × 5) 
24x + 0
= 24x


Step 5 
Right Hand side Vertically Multiplication 
x² + 3x + 5
2x² + 0x+ 8

 = 5 × 8 
= 40

Answer =2x⁴ + 6x³ + 18x² + 24x + 40
(Keep practice and it would be beneficial for you and save time in exams)


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