Answer
$(a-b)^6 = a^6 -6a^5b+15a^4b^2-20a^3b^3+15a^2b^4-6ab^5+b^6$
Work Step by Step
$(a-b)^6$
$(a+b)^n = a^n + n/1!* a^{n-1}*b^1 + n(n-1)/2!* a^{n-2}*b^2 + n(n-1)(n-2)/3!* a^{n-3}*b^3 + . . . + b^n$
$a=a$
$b=-b$
$n=6$
$(a+b)^n = a^n + n/1!* a^{n-1}*b^1 + n(n-1)/2!* a^{n-2}*b^2 + n(n-1)(n-2)/3!* a^{n-3}*b^3 + n(n-1)(n-2)(n-3)/4!* a^{n-3}*b^3+ n(n-1)(n-2)(n-3)(n-4)/5!*a^{n-4}*b^4+ n(n-1)(n-2)(n-3)(n-4)(n-5)/6!*a^{n-5}*b^5+ n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)/6!*a^{n-6}*b^6$
$(a+ (-b))^6 = a^n + n/1!* a^{n-1}*(-b)^1 + n(n-1)/2!*a^{n-2}*(-b)^2 + n(n-1)(n-2)/3!*a^{n-3}*(-b)^3 + n(n-1)(n-2)(n-3)/4!*a^{n-4}*(-b)^4+ n(n-1)(n-2)(n-3)(n-4)/5!*a^{n-4}*(-b)^4+ n(n-1)(n-2)(n-3)(n-4)(n-5)/6!*a^{n-5}*(-b)^5+ n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)/6!*a^{n-6}*(-b)^6$
$(a+ (-b))^6 = a^6 + 6/1!* a^{6-1}*(-b)^1 + 6(6-1)/2!*a^{6-2}*(-b)^2 + 6(6-1)(6-2)/3!*a^{6-3}*(-b)^3 + 6(6-1)(6-2)(6-3)/4!*a^{6-4}*(-b)^4+ 6(6-1)(6-2)(6-3)(6-4)/5!*a^{6-4}*(-b)^4+ 6(6-1)(6-2)(6-3)(6-4)(6-5)/6!*a^{6-5}*(-b)^5+ 6(6-1)(6-2)(6-3)(6-4)(6-5)(6-6)/6!*a^{6-6}*(-b)^6$
$(a+(-b))^6 = a^6 + 6*a^{5}*-b+6(5)/2*a^{4}*b^2 + 6(5)(4)/6*a^{3}*-b^3 + 6(5)(4)(3)/4!*a^2*b^4+ 6(5)(4)(3)(2)/5!*a^1*-b^5+ 6(5)(4)(3)(2)(1)/6!*a^0*b^6$
$(a+(-b))^6 = a^6 -6a^5*b+15a^4b^2 -20a^3b^3 + 15a^2b^4-6ab^5+ b^6$
$(a+(-b))^6 = a^6 -6a^5b+15a^4b^2-20a^3b^3+15a^2b^4-6ab^5+b^6$
