Question

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:
\[
5t(5t + 12v - 3)
\]