Question

Factor the expression completely.
20c2–45

please?

Answer 1

To factor the expression \( 20c^2 - 45 \) completely, we can follow these steps:

1. **Factor out the greatest common factor (GCF)**:
The GCF of \( 20c^2 \) and \( 45 \) is \( 5 \).

So we can factor out \( 5 \):

\[
20c^2 - 45 = 5(4c^2 - 9)
\]

2. **Recognize the remaining expression as a difference of squares**:
The expression \( 4c^2 - 9 \) can be recognized as a difference of squares since it can be rewritten as \( (2c)^2 - 3^2 \).

We can factor it as follows:

\[
4c^2 - 9 = (2c - 3)(2c + 3)
\]

3. **Combine the factors**:
Now we can combine everything we've factored:

\[
20c^2 - 45 = 5(2c - 3)(2c + 3)
\]

Therefore, the completely factored form of the expression \( 20c^2 - 45 \) is:

\[
\boxed{5(2c - 3)(2c + 3)}
\]