 Home > College of Sciences > Institute of Fundamental Sciences > Maths First > Online Maths Help > Algebra > Simple Expansions > The Distributive Law SEARCH MASSEY  # Simple Expansions

## The Distributive Law

We assume that you are familiar with the following exponential rules:

xmxn = xm+n

axmbxn = abxm+n

The method of expansion is based on the distributive law:

a(b + c) = ab + ac             a(b − c) = ab − ac

In particular, when a = –1

(b + c) = b c                 (b − c) = b + c = c – b

### Example 1A.

Here we look at multiplying a number by a linear function. Click on the equal signs to see the expansion:

 ( x + )

### Example 1B.

Multiplying a variable factor by a linear function is done in the same way. Click on the equal signs to see the next step of the expansion:

 ( x + )

### Exercise 1.

Now try a few yourself. Be careful of notation. Do not use spaces in your answer. Write terms in order of highest to lowest power of x.

 Expand the expression: ( x + )    =

 Contact Us | About Massey University | Sitemap | Disclaimer | Last updated: November 21, 2012     © Massey University 2003