Distributive Theory

Algebra is that branch of mathematics in which calculation are made by using any arbitrary characters to stand for the quantities or things considered. The Characters used are generally letters of the English or Greek alphabets and the operations to be performed on the quantities are indicated by signs.

Having problem with Number Theory keep reading my upcoming posts, i will try to help you.

Distributive theory is one of interesting topics in mathematics. It is a process of an expression including more than two occurrences, which are in a row of the any distributive operator. The adding together or reproduction of a set of numbers is the same regardless of how the numbers are grouped.
Definition for Distributive Theory :

Definition:

The distributive theory is a interaction like terms in an algebraic method, we can simply add and multiply their respective coefficients, and the common variable factors. This is actually an application of the distributive property.

Formula:

(a + b) × c = (a × c ) + (b × c)
(a - b) × c = (a × c ) - (b × c)

Distributive theory of Addition:

Example 1 for distributive theory:

Prove that 3 (5 + 7) = (3 x 5) + (3 x 7).

Left hand side:

First take 3 (5 + 7)

By adding 5 + 7 we get 12

And now it is 3 (12)

So the answer for the Left hand side is 36

Right hand side:

Now we take (3 x 5) + (3 x 7)

By multiplying 3 with 5 and 3 with 7 we get (15) + (21)

And now we add 15 with 21

So the answer for Right hand side is 36

Hence proved Left hand side is equal to right hand side.

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Distributive theory of Subtraction:

Example 2 for distributive theory

Prove that 4(9 – 6) = (4 x 9) - (4 x 6).

Left hand side:

First take the 4(9 – 6)

By subtracting 9 – 6 we get 3

And now it is 4 (3)

So the answer for the Left hand side is 12

Right hand side:

Now we take (4 x 9) - (4 x 6)

By multiplying 4 with 9 and 4 with 6 we get (36) - (24)

And now we subtract 36 with 24

So, the answer for Right hand side is 12

Therefore, Left hand side is equal to right hand side.

Hence proved.
Distributive Theory Sample Problems:

Solve the following problems using Distributive theory:

1. Expand using the distributive theory in algebra: a = 3, b = 4, c = 6

Answer: 42

2. Expand using the distributive theory in algebra:  (7 + 5) x 2

Answer: 24

3. Solve the problem using distributive theory: (8 – 4) x 5

Answer: 20

4. Prove the distributive theory: a = 3, b = 6, c = 4

Answer: 36.