81x%5E4-16 Start with the given expression.
%289x%5E2%29%5E2-16 Rewrite 81x%5E4 as %289x%5E2%29%5E2.
%289x%5E2%29%5E2-%284%29%5E2 Rewrite 16 as %284%29%5E2.
Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=9x%5E2 and B=4.
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%5E2%29%5E2-%284%29%5E2=%289x%5E2%2B4%29%289x%5E2-4%29 Plug in A=9x%5E2 and B=4.
So this shows us that 81x%5E4-16 factors to %289x%5E2%2B4%29%289x%5E2-4%29.
In other words 81x%5E4-16=%289x%5E2%2B4%29%289x%5E2-4%29.
Now let's factor 9x%5E2-4 further
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9x%5E2-4 Start with the given expression.
%283x%29%5E2-4 Rewrite 9x%5E2 as %283x%29%5E2.
%283x%29%5E2-%282%29%5E2 Rewrite 4 as %282%29%5E2.
Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=3x and B=2.
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.
%283x%29%5E2-%282%29%5E2=%283x%2B2%29%283x-2%29 Plug in A=3x and B=2.
So this shows us that 9x%5E2-4 factors to %283x%2B2%29%283x-2%29.
In other words 9x%5E2-4=%283x%2B2%29%283x-2%29.
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Answer:
So 81x%5E4-16 completely factors to %289x%5E2%2B4%29%283x%2B2%29%283x-2%29
