Question

Expand the following:

(x + y + 1)³

Answer 1

Given: (x + y + 1)³

Step-wise calculation:

We start by applying the expansion formula for the cube of a trinomial (a + b + c)³.

The general expansion is:

(a + b + c)³ = a³ + b³ + c³ + 3a²b + 3ab² + 3b²c + 3bc² + 3c²a + 3ca² + 6abc

Let: a = x, b = y, c = 1

Calculate each term:

1. a³ = x³
2. b³ = y³
3. c³ = 1³ = 1
4. 3a²b = 3x²y
5. 3ab² = 3xy²
6. 3b²c = 3y² × 1 = 3y²
7. 3bc² = 3y × 1² = 3y
8. 3c²a = 3 × 1² × x = 3x
9. 6abc = 6xy × 1 = 6xy

Now combine all terms:

x³ + y³ + 1 + 3x²y + 3xy² + 3y² + 3y + 3x + 6xy