SOLUTION: Please help me factor completely: {{{(y-5)^2-36q^2}}} Thank you.

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Question 206660: Please help me factor completely:
%28y-5%29%5E2-36q%5E2
Thank you.
Found 2 solutions by Marth, jim_thompson5910:
Answer by Marth(57) About Me  (Show Source):
You can put this solution on YOUR website!
You have the difference of two squares:
%28y-5%29%5E2-36q%5E2

For any two squares a%5E2 and b%5E2, a%5E2-b%5E2 = %28a-b%29%28a%2Bb%29
So for %28y-5%29%5E2-36q%5E2, a=y-5 and b=6q
%28a-b%29%28a%2Bb%29=%28%28y-5%29-6q%29%28%28y-5%29%2B6q%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28y-5%29%5E2-36q%5E2 Start with the given expression.


Let z=y-5


z%5E2-36q%5E2 Replace y-5 with "z"


%28z%29%5E2-36q%5E2 Rewrite z%5E2 as %28z%29%5E2.


%28z%29%5E2-%286q%29%5E2 Rewrite 36q%5E2 as %286q%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=z and B=6q.


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.


%28z%29%5E2-%286q%29%5E2=%28z%2B6q%29%28z-6q%29 Plug in A=z and B=6q.


So this shows us that z%5E2-36q%5E2 factors to %28z%2B6q%29%28z-6q%29.


%28y-5%2B6q%29%28y-5-6q%29 Now plug in z=y-5



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Answer:


So %28y-5%29%5E2-36q%5E2 completely factors to %28y-5%2B6q%29%28y-5-6q%29


In other words %28y-5%29%5E2-36q%5E2=%28y-5%2B6q%29%28y-5-6q%29