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

1 answer

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 \(-2x^2\):

\[ 5x^2 - 2x^2 = 3x^2 \]

  1. Combine \(-3x\) and \(-4x\):

\[ -3x - 4x = -7x \]

  1. 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:

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