Final answer:
To expand the expression (4r+t)^4 using the binomial theorem, we can use the formula (a + b)^n = C(n, 0)a^n + C(n, 1)a^(n-1)b + C(n, 2)a^(n-2)b^2 + ... + C(n, n-2)a^2b^(n-2) + C(n, n-1)ab^(n-1) + C(n, n)b^n. Applying this formula to (4r+t)^4, where a = 4r and b = t, we get 256r^4 + 256r^3t + 96r^2t^2 + 16rt^3 + t^4.
Step-by-step explanation:
To expand the expression (4r+t)^4 using the binomial theorem, we can use the formula:
(a + b)^n = C(n, 0)a^n + C(n, 1)a^(n-1)b + C(n, 2)a^(n-2)b^2 + ... + C(n, n-2)a^2b^(n-2) + C(n, n-1)ab^(n-1) + C(n, n)b^n
Applying this formula to (4r+t)^4, where a = 4r and b = t, we get:
(4r + t)^4 = C(4, 0)(4r)^4 + C(4, 1)(4r)^3(t) + C(4, 2)(4r)^2(t)^2 + C(4, 3)(4r)(t)^3 + C(4, 4)(t)^4
Simplifying further, we have:
256r^4 + 256r^3t + 96r^2t^2 + 16rt^3 + t^4