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? x2+ x+ square feet

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To find the total area of both flowers and vegetables combined, we need to add the two given expressions together.

The areas are:

1. Area of flower beds: \( 3x^2 + 5x - 2 \)
2. Area of vegetable plants: \( 2x^2 - 3x + 4 \)

Now, let's add these two expressions together:

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

Now, we combine like terms:

1. Combine the \( x^2 \) terms:
\[
3x^2 + 2x^2 = 5x^2
\]

2. Combine the \( x \) terms:
\[
5x - 3x = 2x
\]

3. Combine the constant terms:
\[
-2 + 4 = 2
\]

Putting it all together, we get:

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

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

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