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·x – x·3 – 3·x + 3·3)(x·x – x·3 – 3·x + 3·3)
= (x2 – 6x + 9)(x2 – 6x + 9)
= x2(x2 – 6x + 9) – 6x(x2 – 6x + 9) + 9(x2 – 6x + 9)
= x2·x2 – x2·6x + x2·9 – 6x·x2 + 6x·6x – 6x·9 + 9·x2 – 9·6x + 9·9
= x4 – 6x3 + 9x2 – 6x3 + 36x2 – 54x + 9x2 – 54x + 81
= x4 – 12x3 + 54x2 – 108x + 81
|
See
also
Distributing
rules, FOIL method, binomial theorem
