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.