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?

x2

x

Square Feet

1 answer

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.

The total area of the garden is given by: \[ 5x^2 - 3x + 10 \]

The area that belongs to Golden is given by: \[ 2x^2 + 4x - 2 \]

Now, we can calculate the area that belongs to Pablo by subtracting Golden's area from the total area:

\[ \text{Area of Pablo} = \text{Total Area} - \text{Area of Golden} \]

Substituting the expressions:

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

Now we simplify the expression:

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

Next, we combine like terms:

\[ = (5x^2 - 2x^2) + (-3x - 4x) + (10 + 2) \] \[ = 3x^2 - 7x + 12 \]

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

\[ \boxed{3x^2 - 7x + 12} \text{ square feet} \]