Answer
$a^7 - 7 a^6 b + 21 a^5 b^2 - 35 a^4 b^3 + 35 a^3 b^4 - 21 a^2 b^5 + 7 a b^6 - b^7$
Work Step by Step
$(x+y)^n=\binom{n}{0}x^ny^0+\binom{n}{1}x^{n-1}y^1+...+\binom{n}{a}x^{n-a}y^a+..\binom{n}{n}x^{0}y^n$
Here: $n=7$,
$(a-b)^7=\binom{7}{0}a^7(-b)^0+\binom{7}{1}a^{7-1}(-b)^1+\binom{7}{2}a^{7-2}(-b)^2+\binom{7}{3}a^{7-3}(-b)^3+\binom{7}{4}a^{7-4}(-b)^4+\binom{7}{5}a^{7-5}(-b)^5+\binom{7}{6}a^{7-6}(-b)^6+\binom{7}{7}a^{7-7}(-b)^7$
$a^7 - 7 a^6 b + 21 a^5 b^2 - 35 a^4 b^3 + 35 a^3 b^4 - 21 a^2 b^5 + 7 a b^6 - b^7$
