Question

s the statement.

1. $(-5c^{4})cdot(3c^{2})=(3c^{2})cdot(-5c^{4})$
2. $-8k^{2}cdot0 = 0$
3. $(-2x + y)+z=-2x+(y + z)$
4. $-2(4x + 9)=-2(9 + 4x)$
5. $4r^{2}s^{2}+0 = 4r^{2}s^{2}$
6. $-3y+(2y + 7y)=(-3y + 2y)+7y$
7. $(8r + 20s)+0=(20s + 8r)+0$

Explanation:

Step2: Identify Commutative Property of Multiplication

For $(-5c^{4}) \cdot (3c^{2}) = (3c^{2}) \cdot (-5c^{4})$:
This matches the rule $a \cdot b = b \cdot a$, so it is the Commutative Property of Multiplication.

Step4: Identify Multiplicative Property of Zero

For $-8k^{2} \cdot 0 = 0$:
This matches the rule $a \cdot 0 = 0$, so it is the Multiplicative Property of Zero.

Step6: Identify Associative Property of Addition

For $(-2x + y) + z = -2x + (y + z)$:
This matches the rule $(a + b) + c = a + (b + c)$, so it is the Associative Property of Addition.

Step8: Identify Commutative Property of Addition (inside parentheses)

For $-2(4x + 9) = -2(9 + 4x)$:
The terms inside the parentheses are reordered: $4x + 9 = 9 + 4x$, which follows $a + b = b + a$, so it uses the Commutative Property of Addition.

Step10: Identify Additive Identity Property

For $4r^{2}s^{2} + 0 = 4r^{2}s^{2}$:
This matches the rule $a + 0 = a$, so it is the Additive Identity Property.

Step12: Identify Associative Property of Addition

For $-3y + (2y + 7y) = (-3y + 2y) + 7y$:
This matches the rule $(a + b) + c = a + (b + c)$, so it is the Associative Property of Addition.

Step14: Identify Commutative Property of Addition

For $(8r + 20s) + 0 = (20s + 8r) + 0$:
The terms inside the parentheses are reordered: $8r + 20s = 20s + 8r$, which follows $a + b = b + a$, so it uses the Commutative Property of Addition.

Answer:

1. Commutative Property of Multiplication
2. Multiplicative Property of Zero
3. Associative Property of Addition
4. Commutative Property of Addition
5. Additive Identity Property
6. Associative Property of Addition
7. Commutative Property of Addition