Final answer:
To expand the expression (r - t)^4 using the binomial theorem, we can use the formula (a + b)^n = C(n,0)a^n b^0 + C(n,1)a^(n-1) b^1 + C(n,2)a^(n-2) b^2 + ... + C(n,n)a^0 b^n.
Step-by-step explanation:
To expand the expression (r - t)^4 using the binomial theorem, we can use the formula (a + b)^n = C(n,0)a^n b^0 + C(n,1)a^(n-1) b^1 + C(n,2)a^(n-2) b^2 + ... + C(n,n)a^0 b^n, where C(n,r) = n! / (r!(n-r)!).
In this case, a = r, b = -t, and n = 4. Plugging these values into the formula, we have:
(r - t)^4 = C(4,0)r^4 (-t)^0 + C(4,1)r^3 (-t)^1 + C(4,2)r^2 (-t)^2 + C(4,3)r^1 (-t)^3 + C(4,4)r^0 (-t)^4
= r^4 + 4r^3 (-t) + 6r^2 (-t)^2 + 4r (-t)^3 + (-t)^4
= r^4 - 4r^3t + 6r^2t^2 - 4rt^3 + t^4
Therefore, the expanded form of (r - t)^4 is r^4 - 4r^3t + 6r^2t^2 - 4rt^3 + t^4.