Find the LCM of (7+5t),(49-25t^2), and (7t-5t)
The LCM should be divisible by all 3 expressions.
LCM = (49-25t^3) = (7-5t)(7+5t).
CORRECTION: LCM=(49-25t^2)=(7-5t)(7+5t)
To find the LCM (Least Common Multiple) of the given expressions: (7+5t), (49-25t^2), and (7t-5t), we need to follow these steps:
Step 1: Factorize each expression completely and identify the common factors.
Step 2: Identify the highest power of each common factor.
Step 3: Multiply the common factors with their highest powers.
Let's start with each expression:
Expression 1: (7+5t)
This expression is already in its simplest form, and there are no common factors.
Expression 2: (49-25t^2)
This expression is a difference of squares. We can factorize it using the formula: a^2 - b^2 = (a + b)(a - b).
Therefore, (49-25t^2) = (7+5t)(7-5t)
Expression 3: (7t-5t)
This expression simplifies to 2t.
Now, let's identify the highest powers of the common factors:
Common factor 1: (7+5t)
This factor is already simplified, and no power needs to be considered.
Common factor 2: (7-5t)
This factor is already simplified, and no power needs to be considered.
Common factor 3: 2t
This factor has a power of 1.
Now, we multiply the common factors with their highest powers:
LCM = (7+5t)(7-5t)(2t) = (49-25t^2)(2t)
= 98t - 50t^3
Therefore, the LCM of (7+5t), (49-25t^2), and (7t-5t) is 98t - 50t^3.