The problem asks to identify which property of multiplication is represented by the equation $a \times (b + c) = a \times b + a \times c$.

1. Problem Description

The problem asks to identify which property of multiplication is represented by the equation $a \times (b + c) = a \times b + a \times c$.

2. Solution Steps

We need to determine which property is demonstrated by the given equation.

* Associative property: Deals with the grouping of numbers in multiplication or addition: $(a \times b) \times c = a \times (b \times c)$ or $(a + b) + c = a + (b + c)$.

* Identity property: States that any number multiplied by 1 is itself: $a \times 1 = a$. Similarly, any number added to 0 is itself: $a + 0 = a$.

* Closure property: States that performing an operation (like addition or multiplication) on elements within a set results in an element that is also within that set.

* Distributive property: States that multiplying a sum (or difference) by a number is the same as multiplying each addend (or subtrahend) by the number and then adding (or subtracting) the products. $a \times (b+c) = a \times b + a \times c$.

* Commutative property: Deals with the order of numbers in multiplication or addition: $a \times b = b \times a$ or $a + b = b + a$.

The equation $a \times (b + c) = a \times b + a \times c$ illustrates the distributive property.

3. Final Answer

d. Distributive property