Consider the following expression: 2(x + 3) Which of the following represents the correct use of the distributive property? A 2x + 3 B 2x + 6 C x + 6 D x^2 + 6x + 9

Answer

The problem asks to identify the correct use of the distributive property for the expression 2(x + 3). The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. In our given expression, a = 2, b = x, and c = 3. Applying the distributive property: 2(x + 3) = (2 * x) + (2 * 3) = 2x + 6 Now, let's compare this result with the given options: Option A: 2x + 3 (Incorrect, only 'x' was multiplied by 2, not '3') Option B: 2x + 6 (Correct, both 'x' and '3' were multiplied by 2) Option C: x + 6 (Incorrect, the 'x' was not multiplied by 2) Option D: x^2 + 6x + 9 (This is the result of (x+3)^2, not 2(x+3)) Therefore, the correct use of the distributive property is shown in option B. The final answer is \boxed{B}