Integers:

• -3


• 5


• 2

Associative Property for Multiplication:

The associative property of multiplication states that changing the grouping of three or more factors does not change their product. In other words, if we have three integers a, b, and c, then (a × b) × c = a × (b × c).

Let's verify this property for the integers -3, 5, and 2:

(-3 × 5) × 2 = -15 × 2 = -30

-3 × (5 × 2) = -3 × 10 = -30

As we can see, both expressions have the same product, which is -30. Therefore, the associative property of multiplication holds true for the integers -3, 5, and 2.

Distributive Property of Multiplication over Addition:

The distributive property of multiplication over addition states that multiplying a number by the sum of two or more numbers is the same as multiplying the number separately by each of the numbers in the sum and then adding the products. In other words, if we have three integers a, b, and c, then a × (b + c) = (a × b) + (a × c).

Let's verify this property for the integers -3, 5, and 2:

-3 × (5 + 2) = -3 × 7 = -21

(-3 × 5) + (-3 × 2) = -15 + (-6) = -21

As we can see, both expressions have the same result, which is -21. Therefore, the distributive property of multiplication over addition holds true for the integers -3, 5, and 2.

Distributive Property of Multiplication over Subtraction:

The distributive property of multiplication over subtraction states that multiplying a number by the difference of two numbers is the same as multiplying the number separately by each of the numbers in the difference and then subtracting the products. In other words, if we have three integers a, b, and c, then a × (b - c) = (a × b) - (a × c).

Let's verify this property for the integers -3, 5, and 2:

-3 × (5 - 2) = -3 × 3 = -9

(-3 × 5) - (-3 × 2) = -15 + 6 = -9

As we can see, both expressions have the same result, which is -9. Therefore, the distributive property of multiplication over subtraction holds true for the integers -3, 5, and 2.

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