Question
If \( a=1, b=2, c=0 \), find the value of \( a b c-(a+b)+(a-b) \)
Ask by Harris Henry. in Nepal
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value of \( a b c - (a+b) + (a-b) \) is \(-4\).
Solution
1. Substitute the given values into the expression:
\[
a \cdot b \cdot c - (a+b) + (a-b) = 1 \cdot 2 \cdot 0 - (1+2) + (1-2)
\]
2. Calculate the product:
\[
1 \cdot 2 \cdot 0 = 0
\]
3. Evaluate the sum and differences:
\[
(1+2) = 3 \quad \text{and} \quad (1-2) = -1
\]
4. Substitute these results into the expression:
\[
0 - 3 + (-1)
\]
5. Combine the terms:
\[
0 - 3 - 1 = -4
\]
The final answer is:
\[
-4
\]
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Simplify this solution Beyond the Answer
To find the value of the expression \( a b c - (a + b) + (a - b) \) given \( a = 1, b = 2, c = 0 \), we can substitute these values into the expression. First, calculate \( a b c \): \[ a b c = 1 \cdot 2 \cdot 0 = 0 \] Now, calculate \( (a + b) \): \[ a + b = 1 + 2 = 3 \] Next, calculate \( (a - b) \): \[ a - b = 1 - 2 = -1 \] Now, substitute these values into the original expression: \[ a b c - (a + b) + (a - b) = 0 - 3 + (-1) \] Now simplify: \[ 0 - 3 - 1 = -3 - 1 = -4 \] Thus, the final value is \[ \boxed{-4} \]
