To find the area of the garden that belongs to Pablo, we need to subtract the area that belongs to Golden from the total area of the garden.
Given:
- Total area of the garden: \(5x^2 - 3x + 10\)
- Area that belongs to Golden: \(2x^2 + 4x - 2\)
We can represent the area that belongs to Pablo as follows:
\[ \text{Area for Pablo} = \text{Total Area} - \text{Area for Golden} \]
Substituting the given expressions:
\[ \text{Area for Pablo} = (5x^2 - 3x + 10) - (2x^2 + 4x - 2) \]
Now, we distribute the negative sign and simplify:
\[ \text{Area for Pablo} = 5x^2 - 3x + 10 - 2x^2 - 4x + 2 \]
Combine like terms:
- For \(x^2\) terms: \(5x^2 - 2x^2 = 3x^2\)
- For \(x\) terms: \(-3x - 4x = -7x\)
- For constant terms: \(10 + 2 = 12\)
Putting it all together:
\[ \text{Area for Pablo} = 3x^2 - 7x + 12 \]
So, the area of the garden that belongs to Pablo is \(3x^2 - 7x + 12\).