To solve this question, we need to identify which of the given statements represent the distributive property of multiplication. The distributive property states that the multiplication of a number by a sum is equal to the sum of the individual products of the addends and the number. In algebraic terms, this is described as:
[tex]\[ a \times (b + c) = (a \times b) + (a \times c) \][/tex]
Now, let's evaluate each option:
(a) [tex]\( 2 \times 6 = 6 \times 2 \)[/tex]
- This is the commutative property of multiplication, which states that the order of the factors does not change the product.
(b) [tex]\( (2 \times 6) + (2 \times 3) = 2 \times (6 + 3) \)[/tex]
- This correctly exemplifies the distributive property. It shows how multiplying 2 by the sum of 6 and 3 is the same as multiplying 2 by 6 and 2 by 3, then adding the results.
(c) [tex]\( 2 \times 1 = 2 \)[/tex]
- This is the multiplicative identity property, which states that any number multiplied by 1 is itself.
(d) [tex]\( 3 \times (1 + 2) = (3 \times 1) + (3 \times 2) \)[/tex]
- This illustrates the distributive property. It shows a number (3) distributed over the sum (1 + 2).
(e) [tex]\( 3 \times (1 \times 2) = (3 \times 1) \times 2 \)[/tex]
- This is the associative property of multiplication, which shows that the way numbers are grouped in multiplication does not change the product.
(f) [tex]\( 1 \times 3 = 3 \)[/tex]
- This again is the multiplicative identity property.
The statements that show the distributive property are therefore:
(b) [tex]\( (2 \times 6) + (2 \times 3) = 2 \times (6 + 3) \)[/tex]
(d) [tex]\( 3 \times (1 + 2) = (3 \times 1) + (3 \times 2) \)[/tex]
Thus, the correct indices for the distributive property of multiplication are [tex]\([2, 4]\)[/tex].
