Which expression is equivalent to (3a + 4ab - 7b) - (a + 2ab - 4b)?

Rationale

2a + 2ab - 3b

To simplify the expression (3a + 4ab - 7b) - (a + 2ab - 4b), we first distribute the negative sign and then combine like terms, resulting in the expression 2a + 2ab - 3b.

A (2a + 2ab - 11b) YOUR ANSWER

This choice incorrectly combines the terms involving 'b'. After correctly distributing the negative and combining like terms, the correct coefficient for 'b' should be -3, not -11. Therefore, this answer fails to represent the actual simplification.

B (2a + 6ab - 11b) YOUR ANSWER

While the 'a' term and the constant 'b' term are correct in this option, the 'ab' term is incorrect. The correct simplification yields a coefficient of 2 for 'ab', not 6. Hence, this expression does not accurately reflect the original expression's simplification.

C (2a + 2ab - 3b) CORRECT

This choice accurately represents the simplified version of the original expression. After distributing the negative sign and combining like terms, we have 2a for the 'a' terms, 2ab for the 'ab' terms, and -3b for the 'b' terms, making this the correct answer.

D (2a + 6ab - 35) YOUR ANSWER

This choice contains errors in both the 'ab' term and the constant. The term for 'ab' is incorrect, as it should be 2 instead of 6, and there are no constant terms in the expression that would lead to -35. Thus, this answer does not align with the simplification.

Conclusion

The simplification of the expression (3a + 4ab - 7b) - (a + 2ab - 4b) results in 2a + 2ab - 3b, confirming that choice C is the correct answer. Each incorrect option misrepresents the coefficients of the terms involved, emphasizing the importance of careful distribution and combination of like terms in algebraic simplification.

Which expression is equivalent to (3a + 4ab - 7b) - (a + 2ab - 4b)?

2a + 2ab - 3b

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