位置:首页 > SAT > SAT每日一题 > 正文
SAT官方每日一题附答案和解析[数学](2020年2月24日)
日期:2020-02-24 08:53

(单词翻译:单击)

每日一题

Mathematics>Standard Multiple Choice

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)

答案和解析

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=-(-p+1)=-(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).

分享到