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+5)= `
`3x(x) + 3x(5)=`
`3x^2+15x`
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.
Example: 3*37=(3x30)+(3x7)
In Algebra, the Distributive Property helps you simplify expressions with parenthesis.
Example: a(b+c) = ab+ac