## The Example

We want to multiply 4×7. Let’s write it as (4)(7). Then,**Now let’s replace 4 with its equivalent, 3+1. And let’s replace 7 with its equivalent, 5+2. Then,**

(4)(7) = 28

**This seems to be a pretty strange way to write 4×7, doesn’t it? Yet in mathematics – in algebra-style notation – it is just as correct as 4×7. In this form, we can hopefully explain in an understandable way, how the algebra distributive property works.**

(3+1)(5+2) = 28

Refer to the diagram to see how we can do each multiplication and addition in a way that is consistent and can help us to avoid confusion and mistakes.

**Notice (perhaps surprisingly to the beginner) we arrive at the correct answer.**

(3)(5)+(3)(2)+(1)(5)+(1)(2) = (15) + (6) + (5) + (2) = 28

## Generic Format of the Algebra Distributive Property

A simple format for the algebra distributive property if it involves only four simple unknowns is,

(a+b)(c+d) = ac + ad + bc + bd [Answer]

## Our Final Problem

Now, using what we’ve just learned, let’s try a new problem. We will combine constants*and/or*variables to make each of our unknowns. Let’s try,

**Using the order of multiplication we’ve illustrated above, we get**

(3x²+4y)(5x+2)

**or,**

(3x²+4y)(5x+2) = 3x²5x + 3x²2 + 4y5x + 4y2

**Do these really match? For confirmation, let’s pick a value for x and for y, say x = –1 and y =2. Then,**

(3x²+4y)(5x+2) = 15x³ + 6x² + 20yx + 8y [Answer]

**and**

(3x²+4y)(5x+2) = (3(1)+4(2))(5(–1)+2) = **–33**

15x³ + 6x² + 20yx + 8y = –15 + 6 –40 +16 = **–33**

*The results match, as well they should!***Note:** You might also like Mathematical Powers – A Simple Insight

**References:**

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Hey! I can multiply algebra brackets but never even THOUGHT of it in the simple terms like you described 4X7! That’s a good one.

It’s an easy way to start. Dip the toes in, then enter the pool.