Find each of the following products
`5a(6a - 3b)`

Options

A. `30a^2 - 15ab`
B. `30a - 15b`
C. `-30a^2 + 15ab`
D. None of these

Answer

To find the product of the expression \(5a(6a - 3b)\), we will use the distributive property, which states that \(a(b + c) = ab + ac\).

Here are the steps to solve the problem:

### Step 1: Distribute \(5a\) to each term inside the parentheses
We will multiply \(5a\) by both \(6a\) and \(-3b\).

\[ 5a(6a) + 5a(-3b) \]

### Step 2: Calculate the first product \(5a \times 6a\)
When multiplying the coefficients and the variables, we have:

\[ 5 \times 6 = 30 \quad \text{and} \quad a \times a = a^{1+1} = a^2 \]

So,

\[ 5a(6a) = 30a^2 \]

### Step 3: Calculate the second product \(5a \times -3b\)
Again, we multiply the coefficients and the variables:

\[ 5 \times -3 = -15 \quad \text{and} \quad a \times b = ab \]

So,

\[ 5a(-3b) = -15ab \]

### Step 4: Combine the results
Now we combine the two products we calculated:

\[ 30a^2 - 15ab \]

Thus, the final answer is:

\[ \boxed{30a^2 - 15ab} \]

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