At the northwest corner of the park, the city is going to install a fountain. The area of the base of the fountain is 9×2 ? 25 m2 . Factor the area to fi d the lengths of the sides of the fountain.
Answer
🧮 Algebra Made Simple: Factor the Area of the Fountain
The expression for the area of the fountain’s base is given as: 9x² − 25 m²
🔍 Step 1: Identify the Type of Expression
This is a classic example of a difference of squares. Remember, a difference of squares follows this identity:
a² − b² = (a − b)(a + b)
✏️ Step 2: Break Down the Terms
- 9x² is a perfect square because it is equal to (3x)²
- 25 is a perfect square because it is equal to 5²
🧠 Step 3: Apply the Formula
Now apply the difference of squares formula:
9x² − 25 = (3x − 5)(3x + 5)
✅ Final Answer:
The area can be factored as: (3x − 5)(3x + 5)
Therefore, the lengths of the sides of the fountain’s base are:
- (3x − 5) meters
- (3x + 5) meters
💡 Tip for Students: Always look for perfect square patterns in quadratic expressions. It can simplify factorization significantly!