Which of the following expressions is equivalent to the expression 3(a-4)-2(b+8) for all values of a and 47

Rationale

3(a-4)-2(b+8) simplifies to 3a-2b-28.

To simplify the expression, we first distribute the constants through the parentheses: 3(a) - 3(4) - 2(b) - 2(8). This results in the expression 3a - 12 - 2b - 16, which further simplifies to 3a - 2b - 28.

A (3a-2b+4) YOUR ANSWER

This choice incorrectly simplifies the expression, resulting in an addition of 4 instead of the required subtraction of 28. The terms have not been combined correctly, leading to a value that does not reflect the original expression.

B (3a-2b-4) YOUR ANSWER

This option also miscalculates the constant term. While the coefficients of a and b are correct, the constant should be -28, not -4. This indicates that the simplification has not been carried out accurately.

C (3a-2b-20) YOUR ANSWER

Similar to the previous choices, this option misrepresents the constant. The subtraction of 20 is incorrect as the sum of the constants (-12 and -16) should yield -28 instead. Thus, this choice is not equivalent to the original expression.

D (3a-2b-28) CORRECT

This is the correct simplification of the original expression. By distributing and combining like terms correctly, we arrive at 3a - 2b - 28, matching the original expression.

Conclusion

The expression 3(a-4)-2(b+8) simplifies to 3a-2b-28 through proper distribution and combination of like terms. Each incorrect choice fails to accurately reflect the operation applied to the constants, demonstrating the importance of careful algebraic manipulation in confirming equivalency.

Which of the following expressions is equivalent to the expression 3(a-4)-2(b+8) for all values of a and 47

3(a-4)-2(b+8) simplifies to 3a-2b-28.

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