SOLUTION: how do you simplify (xy+ab^2)(xy-ab^2)

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Question 242940: how do you simplify
(xy+ab^2)(xy-ab^2)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You could use the difference of squares formula, but let's do it the long way.




%28x%2Ay%2Ba%2Ab%5E2%29%28x%2Ay-a%2Ab%5E2%29 Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%28x%2Ay%29%2Ba%2Ab%5E2%29%28highlight%28x%2Ay%29-a%2Ab%5E2%29 Multiply the First terms:%28x%2Ay%29%2A%28x%2Ay%29=x%5E2%2Ay%5E2.


%28highlight%28x%2Ay%29%2Ba%2Ab%5E2%29%28x%2Ay%2Bhighlight%28-a%2Ab%5E2%29%29 Multiply the Outer terms:%28x%2Ay%29%2A%28-a%2Ab%5E2%29=-x%2Ay%2Aa%2Ab%5E2.


%28x%2Ay%2Bhighlight%28a%2Ab%5E2%29%29%28highlight%28x%2Ay%29-a%2Ab%5E2%29 Multiply the Inner terms:%28a%2Ab%5E2%29%2A%28x%2Ay%29=x%2Ay%2Aa%2Ab%5E2.


%28x%2Ay%2Bhighlight%28a%2Ab%5E2%29%29%28x%2Ay%2Bhighlight%28-a%2Ab%5E2%29%29 Multiply the Last terms:%28a%2Ab%5E2%29%2A%28-a%2Ab%5E2%29=-a%5E2%2Ab%5E4.


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So we have the terms: x%5E2%2Ay%5E2, -x%2Ay%2Aa%2Ab%5E2, x%2Ay%2Aa%2Ab%5E2, and -a%5E2%2Ab%5E4


x%5E2%2Ay%5E2-x%2Ay%2Aa%2Ab%5E2%2Bx%2Ay%2Aa%2Ab%5E2-a%5E2%2Ab%5E4 Now add every term listed above to make a single expression.


x%5E2%2Ay%5E2-a%5E2%2Ab%5E4 Now combine like terms.


So %28x%2Ay%2Ba%2Ab%5E2%29%28x%2Ay-a%2Ab%5E2%29 FOILs to x%5E2%2Ay%5E2-a%5E2%2Ab%5E4.


In other words, %28x%2Ay%2Ba%2Ab%5E2%29%28x%2Ay-a%2Ab%5E2%29=x%5E2%2Ay%5E2-a%5E2%2Ab%5E4.



Note: recall that the difference of squares formula is %28A%2BB%29%28A-B%29=A%5E2-B%5E2. So you could have used this formula where in this case A=xy and B=ab%5E2