Answer
$(x+y)(x^2-xy+y^2+1)$
Work Step by Step
The formula for factoring the sum of two cubes is: $A^3+B^3=(A+B)(A^2-AB+B^2)$.
Thus: $y^3+x+x^3+y=\\=y^3+x^3+x+y\\=(x+y)(x^2-xy+y^2)+(x+y)(1)\\=(x+y)(x^2-xy+y^2+1)$
Intermediate Algebra for College Students (7th Edition)
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13417-894-7
ISBN 13:
978-0-13417-894-3
Chapter 5 - Section 5.5 - Factoring Special Forms - Exercise Set - Page 373: 133
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