Question

What is the completely factored form of t4 − 16?

Answer 1

we know that

A difference of squares problem can be factored as follows:

`a^(2)-b^(2) =(a+b)(a-b)`

in this problem we have

`t^(4)-16`

Applying difference of squares

`t^(4)-16=(t^(2)-4)( t^(2)+4)`

the term

`(t^(2)-4)=(t+2)(t-2)`

substitute

`(t^(2)-4)( t^(2)+4)=(t+2)(t-2)( t^(2)+4)`

therefore

the answer is

`(t+2)(t-2)( t^(2)+4)`