Question

In 1-2 sentences describe a scenario in which you might need to use the difference of two squares identity to fund the product of two numbers . First describe the general mathematical conditions and explain how you would find x and a then provide a specific real world scenario right it like a tenth grander

Answer 1

The difference of two squares identity states that \( a^2 - b^2 = (a - b)(a + b) \), which is useful when you need to factor or simplify expressions where you have two squared terms. For instance, if you want to calculate the product of \( 14^2 - 6^2 \), you can set \( a = 14 \) and \( b = 6 \) because both numbers are squares (i.e., \( 14^2 = 196 \) and \( 6^2 = 36 \)).

In a real-world scenario, imagine you're creating a rectangular garden where the area is represented by a difference of two squared dimensions—one side is 14 feet long, and the other side is 6 feet shorter. Instead of calculating the area directly, you could use the identity to quickly find that the area, represented by the expression \( 14^2 - 6^2 \), simplifies to \( (14 - 6)(14 + 6) = 8 \times 20 = 160 \) square feet.