Use the distributive property to simplify the expression.
(D) $x(2x+7y)$

• A. $2x^2+7y$
• B. $2x^2+7xy$
• C. $2x+7xy$
• D. $2x^2+7x$

Answer: (B)

Verified step by step guidance

1. Identify the expression where the Distributive Property needs to be applied. The Distributive Property states that for any numbers \(a\), \(b\), and \(c\), the expression \(a(b + c)\) can be rewritten as \(ab + ac\).
2. Look for terms inside parentheses that are being multiplied by a term outside the parentheses. For example, if you have an expression like \(x(y + z)\), you will distribute \(x\) to both \(y\) and \(z\).
3. Multiply the term outside the parentheses by each term inside the parentheses separately. This means calculating \(a \times b\) and \(a \times c\) individually.
4. Rewrite the expression as the sum of the products you found in the previous step. So, \(a(b + c)\) becomes \(ab + ac\).
5. Simplify the expression if possible by combining like terms or performing any additional arithmetic.