Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.5 The Binomial Theorem - 11.5 Assess Your Understanding - Page 857: 23

$x^{10}+5x^8y^2+10x^6y^4+10x^4y^6+5x^2y^8+y^{10}$

Based on the Binomial Theorem, we have $(x^2+y^2)^5=(x^2)^5+5(y^2)(x^2)^4+10(y^2)^2(x^2)^3+10(y^2)^3(x^2)^2+5(y^2)^4(x^2)+(y^2)^5=x^{10}+5x^8y^2+10x^6y^4+10x^4y^6+5x^2y^8+y^{10}$