2019年SAT考试经典数学练习题解析3

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Read the following SAT test question and then click on a button to select your answer.

-(a-1)(b-1)(c-1)

Which of the following is equivalent to the expression above?

A. (1-a)(b-1)(1-c)

B. -(1-c)(1-b)(1-a)

C. (c-1)(1-b)(a-1)

D. -(a-1)(1-b)(c-1)

答案：C

解析：

Choice C is correct. Subtraction is not commutative. (p-1) is not the same as (1-p).

However, it is true that (1-p)=-(p-1): p-1=space-(-p+1) space=space-(1-p)

We can conclude that when the order of two factors being subtracted in an expression is changed, it is the same as multiplying the original expression by-1.

Start with the original expression -1*(a-1)(b-1)(c-1) and change the order of the subtraction for one set of parentheses: -1*-1*(a-1)(1-b)(c-1)=(a-1)(1-b)(c-1)

Multiplication is commutative, so we can reorder the parenthesized groups to get (c-1)(1-b)(a-1).

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