SOLUTION: I need help with this problem please factor each expression y2-81

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Question 88224: I need help with this problem please
factor each expression
y2-81
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2-81 Start with the given expression

Let A%5E2=y%5E2 and B%5E2=81. So we get this:

y%5E2-81=A%5E2-B%5E2

Since A%5E2=y%5E2, A can be solved for:
sqrt%28A%5E2%29=sqrt%28y%5E2%29 Take the square root of both sides

A=y

Since B%5E2=81, B can be solved for:
sqrt%28B%5E2%29=sqrt%2881%29 Take the square root of both sides

B=9

Since we have a difference of squares, we can factor it like this:

A%5E2-B%5E2=%28A%2BB%29%28A-B%29



Now replace A and B
y%5E2-81=%28y%2B9%29%28y-9%29 Plug in A=y and B=9

So the expression

y%5E2-81

factors to

%28y%2B9%29%28y-9%29

Notice that if you foil the factored expression, you get the original expression. This verifies our answer.