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-(a-1)(b-1)(c-1)
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
(1-a)(b-1)(1-c)
(B)
(1-a)(1-b)(1-c)
C)
(a-1)(1-b)(1-c)
(D)
(1-a)(1-b)(c-1)

$-(a-1)(b-1)(c-1)$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $(1-a)(b-1)(1-c)$ $\newline$ (B) $(1-a)(1-b)(1-c)$ $\newline$ C) $(a-1)(1-b)(1-c)$ $\newline$ (D) $(1-a)(1-b)(c-1)$

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Full solution

Q.

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

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

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

\newline

(B)

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

\newline

C)

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

\newline

(D)

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

Given Expression: We are given the expression $-(a-1)(b-1)(c-1)$ and we need to find an equivalent expression among the options provided.
Distribute Negative Sign: Let's distribute the negative sign across the expression. This will change the sign of each term inside the parentheses. $\newline$ $- (a - 1)(b - 1)(c - 1) = (-1) \cdot (a - 1)(b - 1)(c - 1)$
Apply Negative Sign: Now, we apply the negative sign to each term inside the first set of parentheses. $\newline$ (\(-1)\cdot(a $-1$ )(b $-1$ )(c $-1$ ) = ( $1$ -a)(b $-1$ )(c $-1$ )
Compare with Options: We can see that the expression \(1-a)(b $-1$ )(c $-1$ )\ is equivalent to the given expression. Now, let's compare this with the options provided.
Option (A): Option (A) is \(1-a)(b $-1$ )( $1$ -c)\, which is not equivalent to our expression because the sign of the last term c\(-1)\ is different.
Option (B): Option (B) is \(1-a)( $1$ -b)( $1$ -c)\, which is not equivalent to our expression because the signs of the second and third terms are different.
Option (C): Option (C) is a\(-1)( $1$ -b)( $1$ -c)\, which is not equivalent to our expression because the sign of the first term is different.
Option (D): Option (D) is \(1-a)( $1$ -b)(c $-1$ )\, which is not equivalent to our expression because the signs of the second and third terms are different.
Correct Equivalent Expression: The correct equivalent expression is not listed among the options provided. Therefore, none of the options $(A)$ , $(B)$ , $(C)$ , or $(D)$ are equivalent to the given expression $- (a - 1)(b - 1)(c - 1)$ .

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\newline

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