Distributive Property of Multiplication over Addition
Initial Definition

a( b + c ) = ab + ac   and   ( a + b )c = ac + bc,   for all a, b, c is an element of R.

Examples

The distributive property of multiplication over addition.


3(4 + 2) = 3x4 + 3x2

3x6 = 12 + 6

18 = 18

(Both sides have a result of 14.)



The distributive property of multiplication over subtraction.


3(4 - 2) = 3x4 - 3x2

3x2 = 12 - 6

6 = 6

(Both sides have a result of 6.)

Another Example

Multiplication is NOT distributive over multiplication.


3(4 x 2) ≠ 3x4 x 3x2

3x8 ≠ 12 x 6

24 ≠ 72

(Both sides do not have the same result.)



In this case the 3 is distributed to the 4 or the 2, NOT BOTH.


3(4 x 2) = 3x4 x 2

3x8 = 12 x 2

24 = 24

(Both sides have a result of 24.)


3(4 x 2) = 4 x 3x2

3x8 = 4 x 6

24 = 24

(Both sides have a result of 24.)