What is the distributive property?
The distributive property is the ability of multiplication to "distribute" over another operation inside parenthesis. Multiplication distributes over addition or subtraction, such that x(a+b) = xa + xb.
This means we can distribute the factor outside the set of parenthesis to each item inside, and then add the results.
Example: 5(2+3) is equivalent to 5*2 + 5*3 because the multiplication by five was distributed across the addition inside the parenthesis.
Division is not distributive over addition or subtraction
Example: 10/(5-3)`!=` `10/5-10/3`
The Distributive Property can be used in arithmetic to make multiplication easier, breaking up one of the numbers and multiplying two parts separately and then add the products.
In Algebra, the Distributive Property helps you simplify expressions with parenthesis.
Example: a(b+c) = ab+ac
The Distributive Property lets you multiply a sum by multiplying each addend separately and then add the products.
The Distributive Property is handy to help you get rid of parentheses.
a(b + c) = ab + ac
To multiply in algebra, you'll use the distributive law:
`3x(x) + 3x(5)=`
If an expression within a pair of brackets is multiplied by a number, each term within the brackets must be multiplied by that number when the brackets are removed, this is the Distributive Property.
In general, for any 3 integers x, y and z we have x*(y+z)=x * y * x * z. This is called the Distributive law of Multiplication over Addition.
Also, the Distributive Law of Multiplication over Subtraction, that is for any 3 integers x, y and z we have; x*(y-z) = x*y - x*z.
For algebra you can take the following example,
4(a - 2b +3c) = 4a - 8b + 12c.