VEDIC MATHS-91

  

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 91 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Algebraic Calculations-I"

Algebraic Calculations:

Here in this post we will solve algebraic calculations by maths sutra.

Examples :

1. Solve (x + 2)(x + 3) + (x – 6)(x + 5).

Step 1: 

We solve this using the vertically and crosswise method. First, we multiply (x + 2) and (x + 3).

We can either implement the method left to right or from right to left.

(x + 2)

(x + 3)

Going from left to right, we multiply vertically. So we have x times x, which gives us (x)^2. So this is the first part of step 1

Similarly, we do the same for 

(x - 6) 

(x + 5)

that is, we multiply the x’s vertically.

So we have (x)^2 here as well. Adding both these (x)^2 terms we get 2(x)^2.

Step 2:

Now going with the second step, we multiply crosswise. So we have

(x + 2)

(x + 3)

Here we cross-multiply and get three times x plus x times 2. We add 3x + 2x = 5x.

Now we have:

(x - 6)

(x + 5)

Here we cross-multiply and get five times x plus -6 times x. 

We add 5x and -6x and get -x.

Combining the two answers, we get 5x - x = 4x

Step 3:

In our final step, we’ll get +6 by multiplying 3 and 2 together and -30 (by multiplying -6 and 5 together), which gives us -24 as the next part of our answer.

So our answer is (x + 2)(x + 3) + (x - 6)(x + 5) = 2(x)^2 + 4x - 24.

Answer:

(x + 2)(x + 3) + (x - 6)(x + 5) = 2(x)^2 + 4x - 24.

2. Solve (2x – 3)(x + 5) + (x – 1)(x + 3).

Step 1: 

We solve this using the vertically and crosswise method. So first, we multiply vertically the terms which have x

We can either implement the method left to right or from right to left.

(2x - 3)

(x + 5)

So we multiply 2x and x vertically and we get 2(x)^2.

Similarly, we multiply vertically the terms which have x here

(x - 1) 

(x + 3)

that is, we multiply the x’s vertically.

So we have 2(x)^2 here as well. Adding 2(x)^2 + (x)^2 = 3(x)^2.

Step 2:

Now going with the second step, we multiply crosswise. So we have

(2x - 3)

(x + 5)

And get ((5 × 2x) - (3 × x)) = 10x - 3x = 7x.

Similarly, we multiply crosswise

here too mentally:

(x - 1)

(x + 3)

And get (3 × x) + (-1 × x) = 3x - x = 2x.

Combining 7x and 2x gives us 9x.

Step 3:

Finally, we multiply -3 and 5 vertically to get -15. We multiply -1 and 3 vertically to get -3. Combining these two together we get -15 and -3, which equals -18.

So our answer is (x + 2)(x + 3) + (x - 6)(x + 5) = 3(x)^2 + 9x – 18.

Answer:

(2x – 3)(x + 5) + (x – 1)(x + 3) =3(x)^2 + 9x – 18.

Solve the following example.

1. (x – 4)(x + 5) + (x – 1)(x + 3)

Ans : (x – 4)(x + 5) + (x – 1)(x + 3) = 2(x)^2 + 3x – 23.

2. (3x – 6)(x + 5) + (x – 5)(2x + 3)

Ans : (3x – 6)(x + 5) + (x – 5)(2x + 3) =  5(x)^2 + 2x – 45.

3. (3x – 6)(x + 6) + (2x – 5)(2x + 3)

Ans :  (3x – 6)(x + 6) + (2x – 5)(2x + 3) = 7(x)^2 + 8x – 51.

The simplicity of this method can be vouched from examples given above.

You may try following examples.

1. (x – 4)(x + 4) + (x – 3)(x + 1)

2. (2x – 4)(x + 5) + (2x – 5)(x + 3)

3. (2x – 5)(2x + 8) + (3x – 1)(4x + 3)

4. (4x – 4)(8x + 3) + (4x – 1)(7x + 4)

5. (8x – 4)(9x + 1) + (9x – 1)(7x + 8)

In next blog we will discuss about "Algebraic Calculations-II".     

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