Question

which property does each equation demonstrate?
\\(x^2 + 2x = 2x + x^2\\)

\\((3z^4 + 2z^3) - (2z^4 + z^3) = z^4 + z^3\\)

\\((2x^2 + 7x) + (2y^2 + 6y) = (2y^2 + 6y) + (2x^2 + 7x)\\)

associative property
closure property
commutative property

Explanation:

Analyze the first equation

$$ x^2 + 2x = 2x + x^2 $$

$$ A + B = B + A $$

Analyze the second equation

$$ (3z^4 + 2z^3) - (2z^4 + z^3) = z^4 + z^3 $$

$$ P_1 - P_2 = P_3 $$

Analyze the third equation

$$ (2x^2 + 7x) + (2y^2 + 6y) = (2y^2 + 6y) + (2x^2 + 7x) $$

$$ A + B = B + A $$

Answer:

Question 1

For \(x^2 + 2x = 2x + x^2\):
<blank>commutative property</blank>

Question 2

For \((3z^4 + 2z^3) - (2z^4 + z^3) = z^4 + z^3\):
<blank>closure property</blank>

Question 3

For \((2x^2 + 7x) + (2y^2 + 6y) = (2y^2 + 6y) + (2x^2 + 7x)\):
<blank>commutative property</blank>