A student says that his father showed him a very simple method for dealing with expressions like - (a-b+1) and x-(2x-3). The rule is, if there is a negative sign before the parentheses, change the signs of the expressions inside the parentheses. Thus, (a-b+1)= -a+b-1 and x-(2x-3)=x-2x+3. What is your response? Which response is correct? ... OA. By the definition of the associative property of multiplication this statement is incorrect. Therefore, the father is incorrect. O B. By the definition of the distributive property of multiplication over addition and subtraction this statement is incorrect. Therefore, the father is incorrect. OC. By the definition of the distributive property of multiplication over addition and subtraction this statement is incorrect. Therefore, the father is correct. OD. Since for all integers c, -c=(-1)c, the effect of performing the opposite of an algebraic expression is the same as multiplying the expression by - 1. Therefore, the father is correct.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A student says that his father showed him a very simple method for dealing with expressions like - (a - b + 1) and x- (2x - 3). The rule is, if there is a negative sign before the parentheses, change
the signs of the expressions inside the parentheses. Thus, - (a−b+1) = − a+b - 1 and x - (2x − 3) = x - 2x + 3. What is your response?
Which response is correct?
A. By the definition of the associative property of multiplication this statement is incorrect. Therefore, the father is incorrect.
B. By the definition of the distributive property of multiplication over addition and subtraction this statement is incorrect. Therefore, the father is incorrect.
C. By the definition of the distributive property of multiplication over addition and subtraction this statement is incorrect. Therefore, the father is correct.
D. Since for all integers c, -c=(-1)c, the effect of performing the opposite of an algebraic expression is the same as multiplying the expression by - 1. Therefore, the father is correct.
Transcribed Image Text:A student says that his father showed him a very simple method for dealing with expressions like - (a - b + 1) and x- (2x - 3). The rule is, if there is a negative sign before the parentheses, change the signs of the expressions inside the parentheses. Thus, - (a−b+1) = − a+b - 1 and x - (2x − 3) = x - 2x + 3. What is your response? Which response is correct? A. By the definition of the associative property of multiplication this statement is incorrect. Therefore, the father is incorrect. B. By the definition of the distributive property of multiplication over addition and subtraction this statement is incorrect. Therefore, the father is incorrect. C. By the definition of the distributive property of multiplication over addition and subtraction this statement is incorrect. Therefore, the father is correct. D. Since for all integers c, -c=(-1)c, the effect of performing the opposite of an algebraic expression is the same as multiplying the expression by - 1. Therefore, the father is correct.
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