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Distribute
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To multiply out the parts of an expression. Distributing is the opposite of factoring.

Example 1:

3x(x + 8) = 3x·x + 3x·8
                = 3x2 + 24x

Example 2:

(x + 2)(x + 5) = x(x + 5) + 2(x + 5)
                       = x·x + x·5 + 2·x + 2·5
                       = x2 + 7x + 10

Example 3:

(x – 3)4 = (x – 3)(x – 3)(x – 3)(x – 3)
             = (x·xx·3 – 3·x + 3·3)(x·xx·3 – 3·x + 3·3)
             = (x26x + 9)(x26x + 9)
             = x2(x26x + 9) – 6x(x26x + 9) + 9(x26x + 9)
             = x2·x2x2·6x + x2·9 – 6x·x2 + 6x·6x6x·9 + 9·x29·6x + 9·9
             = x4 – 6x3 + 9x2 – 6x3 + 36x2 – 54x + 9x2 – 54x + 81
             = x4 – 12x3 + 54x2 – 108x + 81

 

See also

Distributing rules, FOIL method, binomial theorem

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