Final answer:
The interpretation of '6x + 2 and 3y + 5' depends on the operation between the expressions. Sum implies addition, and product implies multiplication. The correct interpretation cannot be deduced without the actual expression provided.
Step-by-step explanation:
To provide a correct interpretation of the mathematical expression '6x + 2 and 3y + 5,' we must look at the operations mentioned in each statement. Here are the interpretations:
- The sum of 6x + 2 and 3y + 5: This means we should add the two expressions, resulting in 6x + 2 + 3y + 5.
- The product of 6x + 2 and 3y + 5: This indicates multiplying the two expressions together, which would result in (6x + 2)(3y + 5).
- The product of 6 and x + 2(3y + 5): This can be interpreted as 6 times x plus two times the quantity 3y + 5, indicating a multiplication of 6 with x and 2 with (3y + 5) but not multiplying the two expressions 6x and 2(3y + 5) directly with each other.
- The sum of 6x and the product of 2 and 3y + 5: This would mean adding 6x to the result of multiplying 2 with the quantity 3y + 5, or 6x + 2(3y + 5).
Without the actual expression provided, we cannot definitively determine which interpretation is correct. However, in multiplication, when two positive numbers are multiplied, the result is positive (e.g., 2x3 = 6), and the same goes for two negative numbers (e.g., (-4) x (-3) = 12). When numbers with opposite signs are multiplied, the result is negative (e.g., (-3) x 2 = -6). The division follows the same sign rules as multiplication.
Multiplication is also commutative, meaning that the order of multiplication does not change the product (e.g., AxB = BxA). The sum is similarly commutative (A+B = B+A).