Question

Maria is designing a garden for flowers and vegetables. The area of
the garden covered by flower beds can be represented by the
expression 3x² + 5x- 2 square feet. The area of the garden
covered by vegetable plants can be represented by the
expression 2x² - 3x + 4 square feet. What is the total area of both
flowers and vegetables combined?
x+
x+
square feet

Answer 1

To find the total area of both flowers and vegetables in Maria's garden, we need to add the two expressions representing the areas together:

1. The area for flower beds: \(3x^2 + 5x - 2\) square feet
2. The area for vegetable plants: \(2x^2 - 3x + 4\) square feet

Now, we can add these two expressions:

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

Combine like terms:

- **For \(x^2\) terms**: \(3x^2 + 2x^2 = 5x^2\)
- **For \(x\) terms**: \(5x - 3x = 2x\)
- **For constant terms**: \(-2 + 4 = 2\)

Putting it all together, we have:

\[
5x^2 + 2x + 2
\]

So, the total area of both flowers and vegetables combined is:

\[
5x^2 + 2x + 2 \text{ square feet}
\]