Final answer:
Options A (6x+3y) and B (3(x+x+y)) are equivalent to the expression 3x+3(x+y) because they simplify to 6x+3y after applying the distributive property. Option C (3xy) is not equivalent because it introduces multiplication between x and y, which is not in the original expression.
Step-by-step explanation:
The question asks which expressions are equivalent to 3x+3(x+y). To find the equivalent expressions, we need to apply the distributive property to the given expression:
3x + 3(x + y) = 3x + 3x + 3y = 6x + 3y. This shows that 3x+3(x+y) simplifies to 6x+3y. Therefore, option A (6x+3y) is equivalent to the given expression.
Let's inspect option B, which is 3(x + x + y). Again, we apply the distributive property:
3(x + x + y) = 3x + 3x + 3y = 6x + 3y. This demonstrates that option B is also equivalent to the original expression, 3x+3(x+y).
Option C, 3xy, is not equivalent because it implies multiplication between x and y, which is not present in the original expression.