SOLUTION: It is possible to factor x^2 - y^2 by the technique of adding in an extra term, and taking it out again: x^2 - y^2 = x^2 - xy + xy - y^2 = x(x - y) + y(x - y) = (x + y)(x

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Question 1199432: It is possible to factor x^2 - y^2 by the technique of adding in an extra term, and taking it out again:
x^2 - y^2 = x^2 - xy + xy - y^2
= x(x - y) + y(x - y)
= (x + y)(x - y)
Apply this technique to determine a factorization of x^4 - y^4

I'd like to thank Ms.Ikelyn who answered this question previously by using the difference of squares. And while I am thankful for having been provided another perspective, I would also like to know how to factor x^4 - y^4 using that odd "add in a term and take it out again" method. Please let me know how, thank you!
Ref to Ms.Ikelyn's solution: https://www.algebra.com/tutors/students/your-answer.mpl?question=1199431

Answer by ikleyn(53937) (Show Source):
You can put this solution on YOUR website!
.
It is possible to factor x^2 - y^2 by the technique of adding in an extra term, and taking it out again:
x^2 - y^2 = x^2 - xy + xy - y^2
= x(x - y) + y(x - y)
= (x + y)(x - y)
Apply this technique to determine a factorization of x^4 - y^4
I'd like to thank Ms.Ikelyn who answered this question previously by using the difference of squares.
And while I am thankful for having been provided another perspective, I would also like to know
how to factor x^4 - y^4 using that odd "add in a term and take it out again" method. Please let me know how, thank you!
Ref to Ms.Ikelyn's solution: https://www.algebra.com/tutors/students/your-answer.mpl?question=1199431
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x^4 - y^4 = "add and subtract" = (x^4 - x^2*y^2) + (x^2*y^2 - y^4) = x^2*(x^2-y^2) + y^2*(y^2-x^2) = = (x^2-y^2)*(x^2+y^2) = (x+y)*(x-y)*(x^2+y^2). ANSWER

Done and complete in the way you insist.

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It is not another way or another perspective.

It is the same way and the same perspective, but expressed/retold in other words.

The same sock, but only turned inside out.

SOLUTION: It is possible to factor x^2 - y^2 by the technique of adding in an extra term, and taking it out again: x^2 - y^2 = x^2 - xy + xy - y^2 = x(x - y) + y(x - y) = (x + y)(x - y)