Add the following expressions:
`2ab+3bc-5ca, 4bc-3ab+7ca, 2ca-ab-5bc`

Answer

To add the expressions \(2ab + 3bc - 5ca\), \(4bc - 3ab + 7ca\), and \(2ca - ab - 5bc\), we will follow these steps:

### Step 1: Write down the expressions
We start by writing down all the expressions that we need to add together:
\[ 2ab + 3bc - 5ca + 4bc - 3ab + 7ca + 2ca - ab - 5bc \]

### Step 2: Group like terms
Next, we group the like terms together. The like terms are those that contain the same variables:
- Terms with \(ab\): \(2ab, -3ab, -ab\)
- Terms with \(bc\): \(3bc, 4bc, -5bc\)
- Terms with \(ca\): \(-5ca, 7ca, 2ca\)

So we can rewrite the expression as:
\[ (2ab - 3ab - ab) + (3bc + 4bc - 5bc) + (-5ca + 7ca + 2ca) \]

### Step 3: Simplify each group
Now, we simplify each group of like terms:
1. For \(ab\):
\[ 2ab - 3ab - ab = (2 - 3 - 1)ab = -2ab \]

2. For \(bc\):
\[ 3bc + 4bc - 5bc = (3 + 4 - 5)bc = 2bc \]

3. For \(ca\):
\[ -5ca + 7ca + 2ca = (-5 + 7 + 2)ca = 4ca \]

### Step 4: Combine the simplified terms
Now we combine the simplified terms from each group:
\[ -2ab + 2bc + 4ca \]

### Final Answer
Thus, the sum of the given expressions is:
\[ \boxed{-2ab + 2bc + 4ca} \]

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