SOLUTION: how do i simplify (x^2+16)(x^2-16)?

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Question 174836: how do i simplify (x^2+16)(x^2-16)?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This expression represents a difference of squares %28a%2Bb%29%28a-b%29=a%5E2-b%5E2


So %28x%5E2%2B16%29%28x%5E2-16%29=%28x%5E2%29%5E2-%2816%29%5E2=x%5E4-256


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Alternative (slightly longer) Explanation:



%28x%5E2%2B16%29%28x%5E2-16%29 Start with the given expression.


Now let's FOIL the expression.


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


%28highlight%28x%5E2%29%2B16%29%28highlight%28x%5E2%29-16%29 Multiply the First terms:%28x%5E2%29%2A%28x%5E2%29=x%5E4.


%28highlight%28x%5E2%29%2B16%29%28x%5E2%2Bhighlight%28-16%29%29 Multiply the Outer terms:%28x%5E2%29%2A%28-16%29=-16x%5E2.


%28x%5E2%2Bhighlight%2816%29%29%28highlight%28x%5E2%29-16%29 Multiply the Inner terms:%2816%29%2A%28x%5E2%29=16x%5E2.


%28x%5E2%2Bhighlight%2816%29%29%28x%5E2%2Bhighlight%28-16%29%29 Multiply the Last terms:%2816%29%2A%28-16%29=-256.


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x%5E4-16x%5E2%2B16x%5E2-256 Now collect every term to make a single expression.


x%5E4-256 Now combine like terms.


So %28x%5E2%2B16%29%28x%5E2-16%29 FOILs to x%5E4-256.


In other words, %28x%5E2%2B16%29%28x%5E2-16%29=x%5E4-256.