Question
Evaluate the expression if \( x=3, y=-7 \), and \( z=3 \). \( (-2+x)(-1+y)(3-z) \) Select the correct choice below and fill in any answer boxes within your choice. A. \( (-2+x)(-1+y)(3-z)= \) B. The answer is undefined.
Ask by Lambert Lane. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A. \((-2+x)(-1+y)(3-z)= 0\)
Solution
1. Substitute the given values into the expression:
\[
(-2+x)(-1+y)(3-z) \quad \text{with} \quad x=3,\, y=-7,\, z=3.
\]
2. Evaluate each factor:
\[
-2+x = -2+3 = 1,
\]
\[
-1+y = -1+(-7) = -8,
\]
\[
3-z = 3-3 = 0.
\]
3. Multiply the factors together:
\[
1 \cdot (-8) \cdot 0 = 0.
\]
A. \((-2+x)(-1+y)(3-z)= 0\)
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Simplify this solution Extra Insights
First, substitute the values of \( x \), \( y \), and \( z \) into the expression: \[ (-2+3)(-1-7)(3-3) \] Now, simplify each part: 1. \( -2 + 3 = 1 \) 2. \( -1 - 7 = -8 \) 3. \( 3 - 3 = 0 \) Now putting it all together: \[ (1)(-8)(0) \] Since anything multiplied by zero is zero, the final answer is: \[ (-2+x)(-1+y)(3-z) = 0 \] So the correct choice is: A. \( (-2+x)(-1+y)(3-z)= 0 \)
