TRUE OR FALSE

(x+y)+2=2+(x+y)
is it associative property?

(2*3)*5=(3*2)*5
is it commutative property?

(X+3)4=4X+12 is an example of the distributive property of multiplication over addition

(10+y)+z= 10 +(y+z)
is this associative property?

third one is true

2 × 17 = 17 × 2?

To determine whether each equation represents the associative property, commutative property, or distributive property, let's break it down:

1. (x+y)+2=2+(x+y)
This equation represents the commutative property, not the associative property. The commutative property states that the order of the terms can be changed without affecting the result. In this case, the equation is still true regardless of whether (x+y) is placed before 2 or vice versa.

2. (2*3)*5=(3*2)*5
This equation represents the commutative property, not the associative property. Similar to the previous equation, the commutative property applies here because multiplication is commutative, allowing the order of factors to be rearranged without changing the result.

3. (X+3)4=4X+12
This equation represents the distributive property of multiplication over addition. The distributive property states that when a number is multiplied by the sum of two or more numbers, the result is equal to the sum of the products of the number and each addend. In this equation, the expression (X+3) is being multiplied by 4, and the result is equal to the product of 4 and X, plus the product of 4 and 3, which is 4X+12.

4. (10+y)+z=10+(y+z)
This equation represents the associative property, not the commutative property. The associative property states that the grouping of numbers being added or multiplied does not affect the result. In this equation, we can group (10+y) and z together or group 10 and (y+z) together, and the result will be the same, confirming the associative property.