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What is distributive property?

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3 Answers

 The distributive property is easy to show in a simple example which, if used, allows people to do reasonably complicated computations in their head without any need to write them down.

Let's say someone asks you to compute 15*22. Well you can treat this as

15*22 = 15*(20+2) = 15*20+15*2 = 300+30 = 330

What I put in bold is what you would call the distributive property of multiplication with respect to addition.

More in general, using letterals,

a*(b+c) = ab+ac

In your problem, did you mean (6x+3y)*x ? In that case it would be 6x*x + 3y*x = 6x2 + 3xy 

6(x-y) - 3(2x-3y) (distributive property)

= 6x-6y-6x+9y ( 6x and -6x cancel each other out)
= -6y+9y ( add)
= 3y

a(b+c)=ab+ac

The above relation is algebraic way of stating the distributive law or distributive property.  In words, this can be stated as follows:

The result of adding two numbers and multiplying the result by a third number will be the same value as multiplying each of the first two numbers with the third number and adding them together.  This law sometimes provides an easy way to mentally multiply two numbers.  Given the distributive law, I can do the following multiplication by distribution:

27*41=27*40+27*1

Using the distributive law again on the first term (27*40), the above expression becomes

27*41=20*40+7*40+27*1=800+280+27=1107.  Distributive law is applicable to division as well

(1/a)(b+c)=(b/a)+(c/a)