Question

Pablo and Golden are sharing a vegetable garden. The total area of the garden is represented by the expression 5x2−3x+105x2−3x+10. The amount of garden area that belongs to Golden is represented by the expression 2x2+4x−22x2+4x−2. What is area of the garden that belongs to Pablo? x2x2 xx Square Feet

Answer 1

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

1. Total area of the garden: $5x^2-3x+10$
2. Area belonging to Golden: $2x^2+4x-2$

Now, we subtract Golden's area from the total area:

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

Thus, we can write:

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

Now, we distribute the negative sign through Golden's expression:

$$=5x^2-3x+10-2x^2-4x+2$$

Next, we combine like terms:

1. Combine $5x^2$ and $-2x^2$:

$$5x^2-2x^2=3x^2$$

2. Combine $-3x$ and $-4x$:

$$-3x-4x=-7x$$

3. Combine $10$ and $2$:

$$10+2=12$$

Putting it all together, we have:

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

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

$$\boxed{{\displaystyle 3x^2-7x+12}}\text{ square feet}$$