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?

Question

______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:

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