The Distributive Property

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The distributive property is also known as distributive law. “Distribution” the name signifies that the distribution of value to the values inside the bracket. It is very useful in algebra because it makes the expression easier.
 
Distributive property of x, y and z is x (y + z) = xy + xz

Where x has distributed to both the numbers y and z inside the bracket.
 
Example: - Apply the distributive law and find the value of the expression.
            3 x (2 + 5)
 
Solution: - We can distribute 3 to both the values 2 and 5 as
            3 x (2 + 5) = 3 x2 + 3 x 5
                             = 6 +15
                             = 21
So value of the given expression is 21.
 
Example: - Apply the distributive law to the following expression
            9y (10 y^2 + 3 y)

Solution: - We can distribute 9y to both the values 10 y^2 and 3y as
            9y (10 y^2 + 3 y) = 9y *10 y^2 + 9y * 3y
                                       = 90 y^3 + 27 y^2
 
Example: - Use the distributive property for the binomial product.
            (2y + z) (y – z)

Solution: -
            (2y + z) (y – z)= (2y + z) y – (2y + z) z
                                    = 2y^2 + yz – 2yz –z^2
                                    = 2 y^2 – yz – z^2

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