The Distributive Law of Multiplication

Check this out -

8(3 + 5) = (8 * 3) +( 8 * 5)
8(8) = 24 + 40
64 = 64

This pattern is a law. It's something that always hold true. We know this pattern as -

The Distributive Law of Multiplication
a(b + c) = (ab) + (ac)

The word distributive suggests that when you have a multiplier times a sum, you can distribute the multiplier once over each number in the sum!

We can apply the Distributive Law in other ways
to calculate (12 * 7) + (12 * 3).

We know that a(b + c) = (ab) + (ac).
We have an expression in the form (ab) + (ac)
that we can change into a(b + c)!

(12 * 7) + (12 * 3) = 12(7 + 3)
= 12(10)
= 120

Since numbers are commutative and associative under addition and multiplication, The Distributive Law can be written as -

(b + c) a = (ba) + (ca)

It makes no difference what side of the parenthesis the multiplier is on. The final result is always the same!

The Distributive Law is a powerful invaluable tool to add to your math tool kit! It's importance will increase when we explore factoring. Contact us!