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?
______x^2_____x______ Square Feet

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 belonging to Golden: \(2x^2 + 4x - 2\)

We can find Pablo's area by performing the following subtraction:

\[
\text{Area belonging to Pablo} = \text{Total area} - \text{Area belonging to Golden}
\]

Substituting the expressions:

\[
\text{Area belonging to Pablo} = (5x^2 - 3x + 10) - (2x^2 + 4x - 2)
\]

Now, distribute the negative sign:

\[
\text{Area belonging to Pablo} = 5x^2 - 3x + 10 - 2x^2 - 4x + 2
\]

Next, 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:
\[
10 + 2 = 12
\]

So, the expression for the area that belongs to Pablo is:

\[
3x^2 - 7x + 12
\]

Therefore, the area of the garden that belongs to Pablo is:

\[
\boxed{3x^2 \, - \, 7x \, + \, 12 \text{ Square Feet}}
\]