Mathematics>Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
Which of the following is equivalent to the expression above?
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):
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).