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 thar belongs to pablo?

Answer 1

To find the area of the garden that belongs to Pablo, we need to subtract the area belonging to Golden from the total area of the vegetable garden.

Let:
- Total area = \( 5x^2 - 3x + 10 \)
- Area belonging to Golden = \( 2x^2 + 4x - 2 \)

Now, we can calculate the area that belongs to Pablo:

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

\[
= (5x^2 - 3x + 10) - (2x^2 + 4x - 2)
\]

Now, distribute the negative sign across Golden's area:

\[
= 5x^2 - 3x + 10 - 2x^2 - 4x + 2
\]

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

\[
\text{Area belonging to Pablo} = 3x^2 - 7x + 12
\]

Thus, the expression for the area that belongs to Pablo is \( \boxed{3x^2 - 7x + 12} \).