Which expression is equivalent to (st)(6)
The correct Answer and Explanation is:
To simplify the expression ((st)(6)), we follow the basic rules of multiplication. The given expression consists of two parts: (st) and (6). Here’s how we can break it down step by step:
- Identify the Components:
- In the expression (st), (s) and (t) are likely variables, which means they can represent any value. The (6) is a constant number.
- Applying the Distributive Property:
- In multiplication, the order of multiplication does not change the result (commutative property). Therefore, we can rearrange the multiplication without changing the meaning of the expression. Specifically, we can write:
[
(st)(6) = 6(st)
]
or equivalently,
[
(st)(6) = s(6t)
]
or
[
(st)(6) = t(6s)
]
- Final Expression:
- The simplest and most common way to express ((st)(6)) is to multiply the constant with the variable product:
[
6st
]
This is an equivalent expression where the (6) is multiplied by the product of (s) and (t).
- Context and Usage:
- This form (6st) is often used in algebraic contexts where one needs to express a product more clearly. It simplifies calculations in equations or formulas, especially in areas like physics, chemistry, or economics, where multiple variables and constants frequently interact. By expressing the multiplication in a compact form, it’s easier to manipulate equations and understand relationships between variables.
In conclusion, the expression ((st)(6)) simplifies to (6st). This maintains the original value while presenting it in a format that is often more useful for further mathematical operations or interpretations.