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Simple Expansions

The Distributive Law

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

x^mxⁿ = x^m+n

ax^mbxⁿ = abx^m+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:

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:

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.

Expansion Index | Expanding a Pair of Brackets >>