Distributive Property

To multiply a sum (or difference) by the same factor, we multiply each addend (or the minuend and the subtrahend) by that factor and then add (or subtract) the products

The distributive property applies to binary operations such as multiplication and, partially, division.

Distributing multiplication over addition and subtraction

In the case of multiplication, the distributive property states that, given three numbers 𝑎, 𝑏 and 𝑐,

and, symmetrically,

Since multiplication is commutative, it does not matter whether the factor 𝑎 is to the left or the right of the parentheses.

Distributing a factor over a sum

That the sum (𝑎⋅𝑏)+(𝑎⋅𝑐) is equal to 𝑎⋅(𝑏+𝑐) can be understood intuitively through a geometric representation of this equality. Let’s set 𝑎=4, 𝑏=3 and 𝑐=5. For the distributive property, we have:

from which, carrying out the operations, we obtain:

The product 𝑎⋅𝑏 can be represented by a rectangle of area 𝐴=12 and sides 4⋅3. Similarly, the product 𝑎⋅𝑐 by a rectangle of area 𝐴=20 and sides 4⋅5. Thus, the product…