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)

Algebra ->  Customizable Word Problem Solvers  -> Misc -> 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)       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1199431: 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
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

Factoring  x^2 - y^2 = (x+y)*(x-y)  is the standard shortcut, known to all school students of adequate age/grade,

who learn/study Algebra.


So apply this shortcut twice to get

    x^4 - y^4 = (x^2)^2 - (y^2)^2 = (x^2 + y^2)*(x^2 - y^2) = factor (x^2-y^2) again = (x^2 + y^2)*(x+y)*(x-y).

Solved.