Answer
$$=2x^3-x^2-1$$
Work Step by Step
Simplifying and then subtracting the two sides of the expression, we find:
$$x^2\left(x+1\right)^2-\left(x^2+1\right)^2 \\ x^4+2x^3+x^2-\left(x^4+2x^2+1\right) \\ x^4+2x^3+x^2-x^4-2x^2-1 \\ =2x^3-x^2-1$$
Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
by Bittinger, Marvin L.; Ellenbogen, David J.; Johnson, Barbara L.
Published by
Pearson
ISBN 10:
0-32184-874-8
ISBN 13:
978-0-32184-874-1
Chapter 5 - Polynomials and Factoring - 5.4 Factoring Perfect-Square Trinomials and Differences of Squares - 5.4 Exercise Set - Page 334: 117
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