Find the cube of: `3a-2b`

Answer

To find the cube of \(3a - 2b\), we can use the formula for the cube of a binomial, which is given by:

\[ (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3 \]

In our case, we have:
- \(x = 3a\)
- \(y = 2b\)

Now, we will substitute \(x\) and \(y\) into the formula:

\[ (3a - 2b)^3 = (3a)^3 - 3(3a)^2(2b) + 3(3a)(2b)^2 - (2b)^3 \]

Now, let's calculate each term step by step:

1. **Calculate \( (3a)^3 \)**:
\[ (3a)^3 = 27a^3 \]

2. **Calculate \( 3(3a)^2(2b) \)**:
\[ (3a)^2 = 9a^2 \quad \text{so} \quad 3(3a)^2(2b) = 3 \cdot 9a^2 \cdot 2b = 54a^2b \]

3. **Calculate \( 3(3a)(2b)^2 \)**:
\[ (2b)^2 = 4b^2 \quad \text{so} \quad 3(3a)(2b)^2 = 3 \cdot 3a \cdot 4b^2 = 36ab^2 \]

4. **Calculate \( (2b)^3 \)**:
\[ (2b)^3 = 8b^3 \]

Now, we can substitute these values back into the equation:

\[ (3a - 2b)^3 = 27a^3 - 54a^2b + 36ab^2 - 8b^3 \]

Thus, the final answer is:

\[ (3a - 2b)^3 = 27a^3 - 54a^2b + 36ab^2 - 8b^3 \]