What expression is equivalent to 25t^2-15t+60tv

Answer 1

To simplify the expression \( 25t^2 - 15t + 60tv \), we can look for common factors in the terms.

1. First, let's reorder the expression: \( 25t^2 + 60tv - 15t \).
2. Now, we can factor out the greatest common factor (GCF) from the first two terms:
   • The GCF of \( 25t^2 \) and \( 60tv \) is \( 5t \): \[ 5t(5t + 12v) \]
3. Next, we will also factor out \( -15t \) from the third term:
   • Thus, we get: \[ 25t^2 + 60tv - 15t = 5t(5t + 12v) - 15t \]

However, this approach does not combine all the terms effectively based on their structure. Instead, we will look back at the original expression without splitting:

We can actually factor it in a unified way:

1. Notice that \( 25t^2 - 15t + 60tv \) can also be seen as: \[ 25t^2 + 60tv - 15t \]

2. Now we recognize we can reorder this and factor:

   • Combine related terms: \[ 25t^2 + (60v - 15)t \]

3. This helps us identify how to combine them to form a nice quadratic structure: \[ t(25t + 60v - 15) \] This gives us a structured format but not factored completely yet.

However, we can express the original expression \( 25t^2 - 15t + 60tv \) as: \[ 5t(5t + 12v - 3) \] Thus, the expression \( 25t^2 - 15t + 60tv \) can be rewritten as \( 5t(5t + 12v - 3) \).

In conclusion, the equivalent expression is: \[ 5t(5t + 12v - 3) \]