Find the value of :
3ab + 4bc - 5ca when a = 4, b = 5 and c =-2

Answer

To find the value of the expression \(3ab + 4bc - 5ca\) when \(a = 4\), \(b = 5\), and \(c = -2\), we will follow these steps:

### Step 1: Substitute the values of \(a\), \(b\), and \(c\) into the expression.
The expression is:
\[ 3ab + 4bc - 5ca \]
Substituting the values:
\[ 3(4)(5) + 4(5)(-2) - 5(-2)(4) \]

### Step 2: Calculate each term separately.
1. Calculate \(3(4)(5)\):
\[ 3 \times 4 = 12 \quad \text{and then} \quad 12 \times 5 = 60 \]
So, \(3ab = 60\).

2. Calculate \(4(5)(-2)\):
\[ 4 \times 5 = 20 \quad \text{and then} \quad 20 \times (-2) = -40 \]
So, \(4bc = -40\).

3. Calculate \(-5(-2)(4)\):
\[ -5 \times -2 = 10 \quad \text{and then} \quad 10 \times 4 = 40 \]
So, \(-5ca = 40\).

### Step 3: Combine all the calculated terms.
Now we combine the results from the previous calculations:
\[ 60 + (-40) + 40 \]

### Step 4: Simplify the expression.
1. First, add \(60\) and \(-40\):
\[ 60 - 40 = 20 \]
2. Now add \(20\) and \(40\):
\[ 20 + 40 = 60 \]

### Final Answer:
Thus, the value of the expression \(3ab + 4bc - 5ca\) when \(a = 4\), \(b = 5\), and \(c = -2\) is:
\[ \boxed{60} \]