Multiply 3x by (2x + 5y)

Answer

To solve the problem of multiplying \(3x\) by \((2x + 5y)\), we will follow the distributive property of multiplication. Here’s the step-by-step solution:

### Step 1: Write the expression
We start with the expression:
\[ 3x \times (2x + 5y) \]

### Step 2: Apply the distributive property
According to the distributive property, we will multiply \(3x\) by each term inside the parentheses:
\[ 3x \times 2x + 3x \times 5y \]

### Step 3: Multiply \(3x\) by \(2x\)
Now, we multiply \(3x\) by \(2x\):
\[ 3 \times 2 = 6 \quad \text{and} \quad x \times x = x^{1+1} = x^2 \]
So,
\[ 3x \times 2x = 6x^2 \]

### Step 4: Multiply \(3x\) by \(5y\)
Next, we multiply \(3x\) by \(5y\):
\[ 3 \times 5 = 15 \quad \text{and} \quad x \times y = xy \]
So,
\[ 3x \times 5y = 15xy \]

### Step 5: Combine the results
Now, we combine the results from Steps 3 and 4:
\[ 6x^2 + 15xy \]

### Final Answer
Thus, the final answer is:
\[ 6x^2 + 15xy \]

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