SOLUTION: Factor: (w-5)(w+7)+(w-5)(w+9)

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Question 76418: Factor:
(w-5)(w+7)+(w-5)(w+9)
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%28w-5%29%2A%28w%2B7%29%2B%28w-5%29%2A%28w%2B9%29
.
Factor this expression.
.
Note that the two term (separated by the + sign tucked in between the ")" and "(" symbols)
both contain (w-5) as a factor. Therefore this factor of (w-5) can be pulled out as an
overall factor and the result is:
.
%28w-5%29%2A%28%28w%2B7%29%2B%28w%2B9%29%29
.
Since the "(w+7)" and "(w+9)" quantities are both positive quantities, their parentheses
can be removed without changing the terms they contain. Removing these parentheses
results in:
.
%28w-5%29%2A%28w%2B7%2Bw%2B9%29
.
Notice that the quantity on the right within the parentheses can be simplified by adding
the like terms to get:
.
%28w-5%29%2A%282w%2B16%29
.
Then notice that the terms in this simplified quantity have a common factor of 2. So
you can pull this factor out and you have:
.
%28w-5%29%2A2%2A%28w%2B8%29
.
and this can be re-arranged into a more conventional order:
.
2%28w-5%29%28w%2B8%29
.
This is the answer you are looking for.
.
Hope the logical progression from one step to the next one was understandable and that
it provides you with some added insight into the factoring and simplification processes.