The Associative Property pertains to the way in which numbers are grouped in addition or multiplication. It states that the grouping of the numbers does not change the result.
In multiplication, the Associative Property can be illustrated as follows:
\[ a \cdot (b \cdot c) = (a \cdot b) \cdot c \]
Let's analyze the given equations to identify which one demonstrates the Associative Property:
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\(3x \cdot (4x \cdot 5) = (3x \cdot 4x) \cdot 5\): This illustrates the associative property because it shows that regardless of how we group the multiplication, the result remains the same.
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\(3x \cdot (4x + 5x) = (3x + 4x) \cdot 5\): This does not demonstrate the associative property because it involves addition within the parentheses, not multiplication.
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\(3x \cdot (4x \cdot 5) = 3x(4x + 5)\): This one is incorrect because the left side indicates multiplication while the right side indicates a mix of multiplication and addition.
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\((3x + 4x) \cdot 5 = 3x + (4x \cdot 5)\): This also does not demonstrate the associative property—it illustrates the distributive property.
Thus, the correct answer demonstrating the Associative Property is:
\(3x \cdot (4x \cdot 5) = (3x \cdot 4x) \cdot 5\).