SOLUTION: factor 16p^3q-49pq^3

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Question 190760: factor
16p^3q-49pq^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

16p%5E3q-49pq%5E3 Start with the given expression


pq%2816p%5E2-49q%5E2%29 Factor out the GCF pq


Now let's focus on the inner expression 16p%5E2-49q%5E2




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16p%5E2-49q%5E2 Start with the given expression.


%284p%29%5E2-49q%5E2 Rewrite 16p%5E2 as %284p%29%5E2.


%284p%29%5E2-%287q%29%5E2 Rewrite 49q%5E2 as %287q%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=4p and B=7q.


So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:


A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.


%284p%29%5E2-%287q%29%5E2=%284p%2B7q%29%284p-7q%29 Plug in A=4p and B=7q.


So this shows us that 16p%5E2-49q%5E2 factors to %284p%2B7q%29%284p-7q%29.


In other words 16p%5E2-49q%5E2=%284p%2B7q%29%284p-7q%29.


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Answer:
So 16p%5E3q-49pq%5E3 completely factors to pq%284p%2B7q%29%284p-7q%29