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Example: Simplify Using Distributive Law

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Distributive property

In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalizes the distributive law from elementary algebra. For example:

2 × (1 + 3) = (2 × 1) + (2 × 3).

4(8+2) = (4×8) + (4×2) because

4(8 + 2) = 4(10) = 40

(4×8) + (4×2) = 32 + 8 = 40

(Our solved example in mathguru.com uses this concept)

In the left-hand side of the above equation, the 2 multiplies the sum of 1 and 3; on the right-hand side, it multiplies the 1 and the 3 individually, with the results added afterwards. Because these give the same final answer (8), we say that multiplication by 2 distributes over addition of 1 and 3. Since we could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, we say that multiplication of real numbers distributes over addition of real numbers.

http://en.wikipedia.org/wiki/Distributive_property

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.