(2x)yz=2(xy)z property statement
The property statement is: For any values of x, y, and z, the equation (2x)yz is equal to 2(xy)z.
The property statement can be written as follows:
For any real numbers x, y, and z, the equation (2x)yz = 2(xy)z holds true.
The property statement you mentioned is called the associative property of multiplication. This property states that when multiplying three or more numbers together, it doesn't matter how you group them, the product will be the same.
To understand why this property is true, let's break down the given equation and explain step by step:
Starting with the equation (2x)yz = 2(xy)z, we have three variables: x, y, and z.
First, we can simplify the equation by multiplying the terms inside the parentheses:
2 * x * y * z = 2 * x * y * z
Now, we can apply the associative property by re-grouping the terms within the parentheses:
(2 * x) * y * z = 2 * (x * y) * z
Although the grouping has changed, the multiplication is still the same, giving us the property statement you mentioned:
(2x)yz = 2(xy)z
So, in summary, the statement (2x)yz = 2(xy)z is an example of the associative property of multiplication, which states that the grouping of the terms being multiplied doesn't affect the outcome of the product.