Question

Expression: 27w⁸+9w⁴-18w²
GCF: □
Factored Form: □

Answer 1

To solve the expression \( 27w^8 + 9w^4 - 18w^2 \), we will first identify the greatest common factor (GCF) of the terms, and then factor the expression.

**Step 1: Find the GCF**

Let's look at the coefficients of each term:
- The coefficients are 27, 9, and -18.
- The GCF of 27, 9, and 18 is 9.

Next, we look at the variable part:
- The terms are \( w^8 \), \( w^4 \), and \( w^2 \).
- The GCF of \( w^8, w^4, \) and \( w^2 \) is \( w^2 \).

Thus, the GCF of the entire expression \( 27w^8 + 9w^4 - 18w^2 \) is \( 9w^2 \).

**Step 2: Factor out the GCF**

Now that we have the GCF, we can express the original expression in its factored form:

\[
27w^8 + 9w^4 - 18w^2 = 9w^2(3w^6 + w^2 - 2)
\]

Now, let's summarize the results:

**GCF:** \( 9w^2 \)
**Factored Form:** \( 9w^2(3w^6 + w^2 - 2) \)

So, the answers are:

GCF: \( 9w^2 \)
Factored Form: \( 9w^2(3w^6 + w^2 - 2) \)