Question

Sebastian used difference of squares to factor the expression x^4– 16. His work is shown below. His teacher says that he did not "factor completely."How would you explain to Sebastianwhat he needs to do to completely factorthis expression?

Answer 1

To factor properly this expression, we need to use the next expression for the product of the difference of two squares as follows:

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

Since the squares are:

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

We can also see that we have another difference of two squares in the last part of the expression: