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

Question 76418: Factor:
(w-5)(w+7)+(w-5)(w+9)
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
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:
.

.
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:
.

.
Notice that the quantity on the right within the parentheses can be simplified by adding
the like terms to get:
.

.
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:
.

.
and this can be re-arranged into a more conventional order:
.

.
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.
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