Use the area model to factor

20

d

–

16

–

8

f

.

First, find the terms of the factors. The factor on the left must be a whole number greater than 1, and all coefficients must be integers.

20

d

–

16

–

8

f

Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.1234

Now, write

20

d

–

16

–

8

f

in factored form.

Submit

To factor \( 20d - 16 - 8f \) using the area model, we need to break down the expression into terms where a common factor can be identified.

### Step 1: Identify the greatest common factor (GCF)
First, find the GCF of the terms \( 20d \), \( -16 \), and \( -8f \).

- The coefficients of the terms are 20, -16, and -8. The GCF of 20, 16, and 8 is 4.
- Each term can be divided by 4, so the GCF is 4.

### Step 2: Factor out the GCF
Now, factor out 4 from the expression:

\[
20d - 16 - 8f = 4(5d - 4 - 2f)
\]

### Step 3: Verify the factored form
To verify, distribute 4 back into each term:

\[
4(5d - 4 - 2f) = 4 \cdot 5d - 4 \cdot 4 - 4 \cdot 2f = 20d - 16 - 8f
\]

So, the factored form is correct.

### Final Answer:
The factored form of \( 20d - 16 - 8f \) is:

\[
4(5d - 4 - 2f)
\]

Would you like more details or have any questions? Here are some follow-up questions:

1. How do you determine the greatest common factor (GCF) of terms?
2. Can this expression be factored further?
3. Why is factoring useful in solving algebraic equations?
4. What other methods can be used to factor expressions besides the area model?
5. How can you check if your factored expression is correct?

**Tip:** Always check your factoring by distributing back to ensure it matches the original expression.

Use the area model to factor 20d - 16 - 8f. First, find the terms of the factors. The factor on the left must be a whole number greater than 1, and all coefficients must be integers. Now, write 20d - 16 - 8f in factored form.

Learn how to factor the algebraic expression 20d - 16 - 8f using the area model. This problem focuses on identifying the greatest common factor and factoring out common terms. Suitable for students in Grades 6-8.

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