# 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)]
4x- 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 2x + 33x + 4

Now multiply cross wise and add. Shown as under(x × 4) + (3x × 3)
4x + 9x = 13x

Step 3x + 33x + 4

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

So, The answer is = 3x+ 13x + 12

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

[Two Trinomials using (3 × 3)]

Lets another example to understand it
(2x+ x + 5) (3x+ 2x + 6)

Step 1
Write one trinomial under the other as shown below
2x+ x + 5
3x+ 2x + 6
On left hand side column , multiply vertically
2x×  3x= 6x4

Step 2
Now Cross wise multiplication with first two columns
2x+ x + 5
3x+ 2x + 6

= (2x× 2x)  + (3x× x)
= 4x 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

2x+ x + 5
3x+ 2x + 6

= (2x× 6)  + (3x× 5) + ( x × 2x)
= 12x15x+ 2x2
= 29x2

Step 4
Now multiply cross wise middle column with extreme last column (right side)
2x+ x + 5
3x+ 2x + 6

= (2x × 5)  + (x × 6
10x + 6x
= 16x

Step 5
Right Hand side Vertically Multiplication
2x+ x + 5
3x+ 2x + 6

= 5 × 6
= 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
(x+ 3x + 5) (2x+ 8)

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

= x×  2x2
= 2x4

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

= (x× 0x)  + (2x× 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
x+ 3x + 5
2x+ 0x+ 8

= (x× 8)  + (2x× 5) + ( 3x × 0x)
= 8x10x+ 0
= 18x2

Step 4
Now multiply cross wise middle column with extreme last column
x+ 3x + 5
2x+ 0x+ 8

= (3x × 8)  + (0x × 5
24x + 0
24x

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

= 5 × 8
40

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

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