Expanding (x + 3)³
The expression (x + 3)³ represents the product of (x + 3) multiplied by itself three times:
(x + 3)³ = (x + 3)(x + 3)(x + 3)
There are two main ways to expand this expression:
1. Using the distributive property (FOIL method)

Step 1: Expand the first two factors: (x + 3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9

Step 2: Now multiply the result from Step 1 by (x + 3): (x² + 6x + 9)(x + 3) = x²(x + 3) + 6x(x + 3) + 9(x + 3)

Step 3: Distribute and simplify: x³ + 3x² + 6x² + 18x + 9x + 27 = x³ + 9x² + 27x + 27
2. Using the Binomial Theorem
The Binomial Theorem provides a formula for expanding expressions of the form (a + b)ⁿ:
(a + b)ⁿ = ∑(n choose k) a^(nk) b^k
where:
 ∑ represents the sum from k = 0 to n
 (n choose k) is the binomial coefficient, calculated as n! / (k! * (nk)!)
Applying this to our problem:
 a = x, b = 3, n = 3
Therefore:
(x + 3)³ = (3 choose 0) x³ 3⁰ + (3 choose 1) x² 3¹ + (3 choose 2) x¹ 3² + (3 choose 3) x⁰ 3³
Calculating the binomial coefficients:
 (3 choose 0) = 1
 (3 choose 1) = 3
 (3 choose 2) = 3
 (3 choose 3) = 1
Substituting these values back into the equation:
**(x + 3)³ = x³ + 3x² 3 + 3x 9 + 27 = x³ + 9x² + 27x + 27
Conclusion
Both methods lead to the same expanded form of (x + 3)³ which is x³ + 9x² + 27x + 27. Choose the method that you find easiest to apply.