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When a=3 , b=0 , c=-2 , then find ...

When a=3 , b=0 , c=-2 , then find the value of : ab+2bc+3ca+4abc.

A

`-18`

B

`-16`

C

`-20`

D

`-22`

Text Solution

AI Generated Solution

The correct Answer is:
To find the value of the expression \( ab + 2bc + 3ca + 4abc \) when \( a = 3 \), \( b = 0 \), and \( c = -2 \), we will substitute the values of \( a \), \( b \), and \( c \) into the expression step by step. ### Step 1: Substitute the values into the expression The expression is: \[ ab + 2bc + 3ca + 4abc \] Substituting \( a = 3 \), \( b = 0 \), and \( c = -2 \): \[ (3)(0) + 2(0)(-2) + 3(-2)(3) + 4(3)(0)(-2) \] ### Step 2: Calculate each term 1. **Calculate \( ab \)**: \[ ab = 3 \times 0 = 0 \] 2. **Calculate \( 2bc \)**: \[ 2bc = 2 \times 0 \times (-2) = 0 \] 3. **Calculate \( 3ca \)**: \[ 3ca = 3 \times (-2) \times 3 = -18 \] 4. **Calculate \( 4abc \)**: \[ 4abc = 4 \times 3 \times 0 \times (-2) = 0 \] ### Step 3: Add all the terms together Now, we add all the results from the calculations: \[ 0 + 0 - 18 + 0 = -18 \] ### Final Answer The value of the expression \( ab + 2bc + 3ca + 4abc \) when \( a = 3 \), \( b = 0 \), and \( c = -2 \) is: \[ \boxed{-18} \]
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