SOLUTION: Defferences of two squares. How do you factor this binomial? 81x^2-121

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Defferences of two squares. How do you factor this binomial? 81x^2-121      Log On


   

Question 190750: Defferences of two squares.
How do you factor this binomial? 81x^2-121
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713) About Me  (Show Source):
Answer by jim_thompson5910(35256) About Me  (Show Source):
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81x%5E2-121 Start with the given expression.


%289x%29%5E2-121 Rewrite 81x%5E2 as %289x%29%5E2.


%289x%29%5E2-%2811%29%5E2 Rewrite 121 as %2811%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=9x and B=11.


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.


%289x%29%5E2-%2811%29%5E2=%289x%2B11%29%289x-11%29 Plug in A=9x and B=11.


So this shows us that 81x%5E2-121 factors to %289x%2B11%29%289x-11%29.


In other words 81x%5E2-121=%289x%2B11%29%289x-11%29.