Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.5 The Binomial Theorem - 11.5 Assess Your Understanding - Page 857: 24

$x^{12}-6x^{10}y^2+15x^8y^4-20x^6y^6+15x^4y^8-6x^2y^{10}+y^{12}$

Based on the Binomial Theorem, we have $(x^2-y^2)^6=(x^2)^6-6(y^2)(x^2)^5+15(y^2)^2(x^2)^4-20(y^2)^3(x^2)^3+15(y^2)^4(x^2)^2-6(y^2)^5(x^2)+(y^2)^6=x^{12}-6x^{10}y^2+15x^8y^4-20x^6y^6+15x^4y^8-6x^2y^{10}+y^{12}$