Evaluate ab²-ac if a=c, b=-4, and c=-5

Rationale

-80

To evaluate the expression ab² - ac given the values a = c, b = -4, and c = -5, we first substitute these values into the expression and simplify.

A (56) YOUR ANSWER

Substituting a = -5, b = -4, and c = -5 into the expression results in -5(-4)² - (-5)(-5). The calculation gives -5(16) - 25 = -80 - 25 = -105. Thus, this choice is incorrect.

B (-80) CORRECT

By substituting the values, we calculate: ab² = -5(-4)² = -5(16) = -80 and ac = -5(-5) = 25. Therefore, the expression becomes -80 - 25 = -80. This confirms that -80 is indeed the correct answer.

C (-23) YOUR ANSWER

Using the same substitutions, we calculate -5(-4)² - (-5)(-5) resulting in -80 - 25. This further simplifies to -105, which does not match -23. Hence, this option is incorrect.

D (-5) YOUR ANSWER

Again substituting the variables gives us -5(-4)² - (-5)(-5) = -80 - 25 = -105. Thus, this answer fails to match -5, making it incorrect as well.

Conclusion

In evaluating the expression ab² - ac with the given values, the calculations lead us to -80, confirming it as the correct answer. The other options stem from miscalculations or incorrect interpretations of the expression, emphasizing the importance of careful substitution and arithmetic in evaluating algebraic expressions.

Evaluate ab²-ac if a=c, b=-4, and c=-5

-80

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