4. Which of the following expressions is equivalent to the expression 3(a-4)-2(b+8) for all values of a and 47
Answer: D
3a-2b-28
The expression equivalent to 3(a-4)-2(b+8) for all values of a and b simplifies to 3a-2b-28.
A) 3a-2b+4
This option is incorrect because it does not accurately reflect the simplification of the original expression. The term -4 from 3(a-4) and +16 from -2(b+8) should result in -28, not +4.
B) 3a-2b-4
Option B is also incorrect. While it maintains the correct form of 3a-2b, the constant term is incorrect as it omits the necessary adjustments from both components of the expression.
C) 3a-2b-20
This option is incorrect as well. The expression fails to account for the full simplification of the original expression, specifically the effects of the -2(b+8) part, which leads to an incorrect constant term.
D) 3a-2b-28
Option D is the correct answer. It accurately represents the simplified form of the expression 3(a-4)-2(b+8), where the calculations yield -28 as the final constant term after distributing and combining like terms.
Conclusion
Option D is definitively correct as it properly simplifies the original expression to 3a-2b-28, reflecting the contributions of both terms accurately. All other options fail to represent the correct simplification, either by miscalculating the constant or altering the expression's structure incorrectly.