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anonymous
 one year ago
What is the completely factored form of t4 − 16?
anonymous
 one year ago
What is the completely factored form of t4 − 16?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes. I got (t24)(t2+4)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait! No it's not. I got it wrong:(

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1i was thinking both of them are the same thing

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1what was the right answer?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1:) welcome to openstudy :)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Factoring means factoring completely. When you have to factor a polynomial of two terms, look for the difference of squares or the sum or difference of cubes. The first step in factoring, though, is always to look for a common factor. In this case there is no common factor. Then you have two terms. t^4 is obviously not a cube, so look at the difference of two squares. Sure enough, \(t^4  16\) can be written as \( (t^2)  4^2 \) which clearly looks like the difference of two squares.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0The difference of squares factors like this: \(a^2  b^2 = (a + b)(a  b) \) Your expression factors similarly: \((t^2)^2  4^2 = (t^2 + 4)(t^2  4) \) Now you need to look at each factor to see if it can be factored further. \(t^2 + 4\) is a sum of squares. It can't be factored. Now we look at \(t^2  4\) which is a difference of squares and can be factored. \(t^4  16 = (t^2)^2  4^2 = (t^2 + 4)(t^2  4) = (t^2 + 4)(t + 2)(t  2) \) Finally we look at the new factors, t + 2 and t  2, and we see that they can;t be factored any further, so our answer above is fully factored.
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