Question

Pablo and Golden are sharing a vegetable garden. The total area of the garden is represented by the expression 5x^2 - 3x + 10. The amount of garden area that belongs to Golden is represented by the expression. 2x^2 + 4x - 2. What is area of the garden that belongs to Pablo?

Answer 1

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:

1. For \(x^2\) terms: \(5x^2 - 2x^2 = 3x^2\)
2. For \(x\) terms: \(-3x - 4x = -7x\)
3. 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 \(3x^2 - 7x + 12\).