Answer
$x^{12}-6x^{10}y^2+15x^8y^4-20x^6y^6+15x^4y^8-6x^2y^{10}+y^{12}$
Work Step by Step
We are given the expression:
$(x^2-y^2)^6$
Use the Binomial Theorem to expand the expression:
$(x^2-y^2)^6=\sum_{k=0}^6 \binom{6}{k}(x^2)^{6-k}(-y^2)^k$
$=\binom{6}{0}(x^2)^6(-y^2)^0+\binom{6}{1}(x^2)^5(-y^2)^1+\binom{6}{2}(x^2)^4(-y^2)^2+\binom{6}{3}(x^2)^3(-y^2)^3+\binom{6}{4}(x^2)^2(-y^2)^4+\binom{6}{5}(x^2)^1(-y^2)^5+\binom{6}{6}(x^2)^0(-y^2)^6$
$=x^{12}-6x^{10}y^2+15x^8y^4-20x^6y^6+15x^4y^8-6x^2y^{10}+y^{12}$
