Question 76418
Given:
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{{{(w-5)*(w+7)+(w-5)*(w+9)}}}
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Factor this expression.
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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:
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{{{(w-5)*((w+7)+(w+9))}}}
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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:
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{{{(w-5)*(w+7+w+9)}}}
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Notice that the quantity on the right within the parentheses can be simplified by adding
the like terms to get:
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{{{(w-5)*(2w+16)}}}
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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:
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{{{(w-5)*2*(w+8)}}}
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and this can be re-arranged into a more conventional order:
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{{{2(w-5)(w+8)}}}
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This is the answer you are looking for.
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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.