Expanding the expression (a-b)^6 using the binomial theorem, we have:
(a-b)^6 = (6 choose 0) a^6 (-b)^0 +(6 choose 1) a^5 (-b)^1 +(6 choose 2) a^4 (-b)^2 +(6 choose 3) a^3 (-b)^3 +(6 choose 4) a^2 (-b)^4 +(6 choose 5) a^1 (-b)^5 +(6 choose 6) a^0 (-b)^6
Which simplifies to:
a^6 - 6a^5b + 15a^4b^2 - 20a^3b^3 + 15a^2b^4 - 6ab^5 + b^6
Expanding the expression (a-b)^6 using the binomial theorem, we have:
(a-b)^6 =
(6 choose 0) a^6 (-b)^0 +
(6 choose 1) a^5 (-b)^1 +
(6 choose 2) a^4 (-b)^2 +
(6 choose 3) a^3 (-b)^3 +
(6 choose 4) a^2 (-b)^4 +
(6 choose 5) a^1 (-b)^5 +
(6 choose 6) a^0 (-b)^6
Which simplifies to:
a^6 - 6a^5b + 15a^4b^2 - 20a^3b^3 + 15a^2b^4 - 6ab^5 + b^6