Find the cube of `(2a-3b)`

Explanation

To find the cube of \( (2a - 3b) \), we will 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 can identify:
- \( x = 2a \)
- \( y = 3b \)

So, we can rewrite the expression as:

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

Now, applying the formula:

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

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

1. **Calculate \( (2a)^3 \)**:
\[ (2a)^3 = 2^3 \cdot a^3 = 8a^3 \]

2. **Calculate \( 3(2a)^2(3b) \)**:
\[ 3(2a)^2(3b) = 3 \cdot 4a^2 \cdot 3b = 36a^2b \]

3. **Calculate \( 3(2a)(3b)^2 \)**:
\[ 3(2a)(3b)^2 = 3 \cdot 2a \cdot 9b^2 = 54ab^2 \]

4. **Calculate \( (3b)^3 \)**:
\[ (3b)^3 = 27b^3 \]

Now, substituting these values back into the expression:

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

Thus, the final result is:

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