Multiply each expression.
$3a(5a+3b)$

• A. $15a^2+3ab$
• B. $9a^2+15ab$
• C. $15a^2+9ab$
• D. $9a^2+9ab$

Answer: (C)

Verified step by step guidance

1. Identify the monomial and the polynomial in the expression you need to multiply. The monomial is a single term (like \$3x^2\(), and the polynomial is a sum of terms (like \)2x + 5$).
2. Apply the distributive property, which means you multiply the monomial by each term inside the polynomial separately. For example, if you have \(a\) times \((b + c)\), you calculate \(a \times b\) and \(a \times c\).
3. Multiply the coefficients (numbers) together. For example, if you multiply \(3\) and \(2\), you get \(6\).
4. Multiply the variables by adding their exponents when the bases are the same. For example, \(x^2 \times x^3 = x^{2+3} = x^5\).
5. Write the final expression by combining all the products from the previous steps, ensuring each term is simplified and correctly written.