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.
(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
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
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
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
(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
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
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
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)
Read 10 Vedic Maths Tricks
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