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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?

Sebastian used difference of squares to factor the expression x4 16 His work is shown below His teacher says that he did not factor completelyHow would you expl class=

Respuesta :

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

[tex]a^2-b^2=(a+b)\cdot(a-b)[/tex]

Since the squares are:

[tex](x^2)^2-(4)^2=(x^2+4)(x^2-4)[/tex]

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

[tex]undefined[/tex]

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