Expanding (x + 4)^3
Expanding (x + 4)^3 means multiplying (x + 4) by itself three times:
(x + 4)^3 = (x + 4)(x + 4)(x + 4)
There are two main ways to solve this:
1. Using the Binomial Theorem:
The Binomial Theorem provides a formula to expand expressions of the form (x + y)^n. It states:
(x + y)^n = Σ (n choose k) * x^(nk) * y^k, where:
 n is the power
 k ranges from 0 to n
 (n choose k) represents the binomial coefficient, calculated as n! / (k! * (nk)!)
Applying this to our case (x + 4)^3:
 n = 3
 k = 0, 1, 2, 3
Let's expand:
 k = 0: (3 choose 0) * x^(30) * 4^0 = 1 * x^3 * 1 = x^3
 k = 1: (3 choose 1) * x^(31) * 4^1 = 3 * x^2 * 4 = 12x^2
 k = 2: (3 choose 2) * x^(32) * 4^2 = 3 * x^1 * 16 = 48x
 k = 3: (3 choose 3) * x^(33) * 4^3 = 1 * x^0 * 64 = 64
Adding all the terms together:
(x + 4)^3 = x^3 + 12x^2 + 48x + 64
2. Expanding step by step:

Step 1: Expand (x + 4)(x + 4)
 (x + 4)(x + 4) = x(x + 4) + 4(x + 4) = x^2 + 4x + 4x + 16 = x^2 + 8x + 16

Step 2: Multiply the result by (x + 4)
 (x^2 + 8x + 16)(x + 4) = x(x^2 + 8x + 16) + 4(x^2 + 8x + 16)
 = x^3 + 8x^2 + 16x + 4x^2 + 32x + 64
 = x^3 + 12x^2 + 48x + 64
Both methods arrive at the same answer: (x + 4)^3 = x^3 + 12x^2 + 48x + 64