give me a word problem that includes factoring special products

Here’s a word problem that involves factoring special products:

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**Problem:**

A rectangular garden has a length that is 6 meters longer than its width. The total area of the garden is 144 square meters. Find the dimensions of the garden.

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**Solution Outline:**

To solve this, you would set up an equation based on the formula for the area of a rectangle:  
Area = Length × Width.

Let the width be \( w \) meters.  
Then the length is \( w + 6 \) meters.  
Thus, the area equation is:

\[
w(w + 6) = 144
\]

Expanding this, we get:

\[
w^2 + 6w = 144
\]

Now, subtract 144 from both sides to set the equation equal to 0:

\[
w^2 + 6w - 144 = 0
\]

This is a quadratic equation, which can be factored (if possible) to find the value of \( w \).

Would you like to proceed with solving this, or do you have any questions?

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**Related Questions:**

1. What are some other examples of factoring special products?
2. Can all quadratic equations be factored easily?
3. How would the problem change if the length was 10 meters longer than the width?
4. How do you solve quadratic equations using the quadratic formula?
5. What are the different types of special products in algebra?

**Tip:** Factoring special products can often be quicker than using the quadratic formula, but it requires recognizing patterns like perfect squares or difference of squares.

This problem involves solving a quadratic equation by factoring special products. Learn how to find the dimensions of a garden with a length 6 meters longer than its width and an area of 144 square meters. This problem is suitable for students in Grades 8-10 and covers key algebraic concepts, including factoring and quadratic equations.

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