To determine which of the given options illustrates the commutative property of multiplication, let's review the commutative property first. The commutative property of multiplication states that changing the order of factors does not change the product. In other words, for any two numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[ a \times b = b \times a \][/tex]
Let's evaluate each of the options provided:
### Option A: [tex]\(6(5-2) = 5(6-2)\)[/tex]
First, we need to simplify both sides of the equation.
Left side:
[tex]\[ 6(5-2) = 6 \times 3 = 18 \][/tex]
Right side:
[tex]\[ 5(6-2) = 5 \times 4 = 20 \][/tex]
Since [tex]\(18 \ne 20\)[/tex], this option does not demonstrate the commutative property of multiplication.
### Option B: [tex]\(112 + 271 = 271 + 112\)[/tex]
This equation involves addition, not multiplication. It is an example of the commutative property of addition, not multiplication. Thus, this option is not relevant to our problem.
### Option C: [tex]\(8(8+8) = 8(8-8)\)[/tex]
Again, let's simplify both sides of the equation.
Left side:
[tex]\[ 8(8+8) = 8 \times 16 = 128 \][/tex]
Right side:
[tex]\[ 8(8-8) = 8 \times 0 = 0 \][/tex]
Since [tex]\(128 \ne 0\)[/tex], this option does not demonstrate the commutative property of multiplication.
### Option D: [tex]\(2 \times 8 = 8 \times 2\)[/tex]
Let's compute both sides of the equation.
Left side:
[tex]\[ 2 \times 8 = 16 \][/tex]
Right side:
[tex]\[ 8 \times 2 = 16 \][/tex]
Since [tex]\(16 = 16\)[/tex], this option does demonstrate the commutative property of multiplication.
Thus, the correct answer is:
Option D: [tex]\(2 \times 8 = 8 \times 2\)[/tex]
