Find the cube of: `5a +3b`

Answer

To find the cube of \(5a + 3b\), we will use the formula for the cube of a binomial, which is:

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

In this case, let \(x = 5a\) and \(y = 3b\).

### Step 1: Identify \(x\) and \(y\)
Let:
- \(x = 5a\)
- \(y = 3b\)

### Step 2: Apply the formula
Using the formula, we can substitute \(x\) and \(y\):

\[ (5a + 3b)^3 = (5a)^3 + (3b)^3 + 3(5a)^2(3b) + 3(5a)(3b)^2 \]

### Step 3: Calculate each term
1. **Calculate \( (5a)^3 \)**:
\[ (5a)^3 = 5^3 \cdot a^3 = 125a^3 \]

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

3. **Calculate \( 3(5a)^2(3b) \)**:
\[ 3(5a)^2(3b) = 3 \cdot 25a^2 \cdot 3b = 225a^2b \]

4. **Calculate \( 3(5a)(3b)^2 \)**:
\[ 3(5a)(3b)^2 = 3 \cdot 5a \cdot 9b^2 = 135ab^2 \]

### Step 4: Combine all the terms
Now we can combine all the calculated terms:

\[ (5a + 3b)^3 = 125a^3 + 27b^3 + 225a^2b + 135ab^2 \]

### Final Result
Thus, the cube of \(5a + 3b\) is:

\[ (5a + 3b)^3 = 125a^3 + 27b^3 + 225a^2b + 135ab^2 \]

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