The distributive property states that:

a ⋅ (b + c) = (a ⋅ b) + (a ⋅ c)

Then applying the Symmetric Property of Equality, we conclude that:

(a ⋅ b) + (a ⋅ c) = a ⋅ (b + c)

For example, let's try to simplify the following:

(x ⋅ 2) + (x ⋅ 3)

Using the variation above, we claim that:

(x ⋅ 2) + (x ⋅ 3) = x ⋅ (2 + 3)

= x ⋅ 5

Here is another variation of the distributive property:

(b ⋅ a) + (c ⋅ a) = (b + c) ⋅ a

For example, let's try to simplify the following:

(2 ⋅ y) + (5 ⋅ y)

Using the variation above, we claim that:

(2 ⋅ y) + (5 ⋅ y) = (2 + 5) ⋅ y

= 7 ⋅ y