Problem 140 Factor completely. $$x^{4}-y^{... [FREE SOLUTION]

Chapter 0: Problem 140

Factor completely. $$x^{4}-y^{4}-2 x^{3} y+2 x y^{3}$$

Short Answer

Expert verified

The factorization of the original polynomial is $(x^{2} - y^{2} - xy)(x^{2} - y^{2} + xy)$.

Step by step solution

Rearrange the Terms

Rearrange the terms in such a way that we get two difference of squares: $x^{4} -2 x^{3} y + 2x y^{3} - y^{4}$. This is simply the same polynomial as above but rearranged.

Factor Using Difference of Squares

Take first two and last two terms separately and factor them using the formula for difference of squares. On applying, we get $(x^{2} - y^{2})^{2} - (x y)^{2}$.

Apply Difference of Squares Again

Recognize this as another difference of squares, and apply the formula again: $(x^{2} - y^{2} - xy)(x^{2} - y^{2} + xy)$. The polynomial is now factored completely.

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91影视

Factor completely. $$x^{4}-y^{4}-2 x^{3} y+2 x y^{3}$$

Short Answer

Step by step solution

Rearrange the Terms

Factor Using Difference of Squares

Apply Difference of Squares Again

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