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Year 10 Interactive Maths - Second Edition


Expanding Three Terms

Consider the expansion of the expression 4(x + 3)(x + 2). The simplest way to expand three such terms is to expand the binomial product (x + 3)(x + 2) and then multiply the resulting terms with the number 4 as follows:

Expanding 4(x + 3)(x + 2).


Example 8

Expand (x + 4)(x + 3)(x - 3).

Solution:

(x + 4)(x + 3)(x - 3) is expanded by first using the Distributive Law to expand (x + 3)(x - 3). Then the Distributive Law is applied again to expand the resulting binomial product. The solution is written in descending powers of x.

Alternatively:

We can expand as follows:

(x + 4)(x + 3)(x - 3) is expanded by first using the difference of two squares formula to expand (x + 3)(x - 3). Then the Distributive Law is applied to expand the resulting binomial product. The solution is written in descending powers of x.

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