(55.25)2 - 637.5625 = ?

Concept

For any two numbers a and b, the difference of squares identity states: a2 - b2 = (a + b)(a - b). Recognizing when a subtraction of squares fits this pattern turns a lengthy squaring calculation into a quick multiplication.

Application

1. The expression to evaluate is (55.25)2 - 637.5625.

2. Since 25.25 x 25.25 = 637.5625, the number 637.5625 is (25.25)2.

3. The expression now matches the a2 - b2 pattern with a = 55.25 and b = 25.25, so it factors as (55.25 + 25.25)(55.25 - 25.25).

4. Simplify each bracket: 55.25 + 25.25 = 80.5 and 55.25 - 25.25 = 30.

5. Multiply the two results: 80.5 x 30 = 2415.

Cross-check

Confirming by direct computation: (55.25)2 = 3052.5625, and 3052.5625 - 637.5625 = 2415, the same result as the factored calculation.

So the value of the expression is 2415.