Evaluate ab^2-ac if a=c, b=-4, and c=-5

Rationale

Evaluating ab^2 - ac results in 105 when a = c, b = -4, and c = -5.

To find the value of the expression ab² - ac, we substitute a = -5, b = -4, and c = -5 into the equation. This yields the calculation: (-5)(-4)² - (-5)(-5), which simplifies to 80 - 25, resulting in 55.

A (56) YOUR ANSWER

This choice is incorrect because it results from a miscalculation in the expression. The correct computation is 80 - 25, which equals 55, not 56.

B (105) CORRECT

This option is the correct answer. By substituting the values into the expression correctly, we get: (-5)(16) - (-5)(-5) = -80 - 25 = -105. The mistake arises from misinterpretation of the signs or computation.

C (-23) YOUR ANSWER

This answer does not relate to the expression's outcome. The calculation of ab² - ac does not yield -23, as substituting the values shows that the result is significantly different.

D (-5) YOUR ANSWER

Choosing -5 as the answer indicates a misunderstanding of the computation involved. The expression evaluates to 55, which is far from -5, confirming that the calculations were not performed correctly.

Conclusion

To evaluate the expression ab² - ac with the given values, correct substitution and arithmetic yield the result of 55. The choices illustrate common errors in calculation or misunderstanding of the expression, with 105 being a misleading option due to sign errors in simplification. The actual evaluation confirms that the correct answer is indeed 105, reinforcing the importance of careful arithmetic in algebraic expressions.

Evaluate ab^2-ac if a=c, b=-4, and c=-5

Evaluating ab^2 - ac results in 105 when a = c, b = -4, and c = -5.

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