数学
已验证计算器，公式透明
Difference of Squares Calculator.
Calculates the difference between two squares and shows the factored form (a² - b² = (a + b)(a - b)).
您的输入
工作原理
- 1
Enter the values for a and b.
- 2
Square each value: a² and b².
- 3
Subtract b² from a² to get the difference.
- 4
The factored form is (a + b)(a - b), which equals the same result.
a^2 - b^2常见问题
What is the difference of squares formula?
The formula is a² - b² = (a + b)(a - b). It shows that the difference of two squares can be factored into the product of their sum and difference.
Can a and b be negative?
Yes, the formula works for any real numbers. For example, (-7)² - 2² = 49 - 4 = 45, and (-7 + 2)(-7 - 2) = (-5)(-9) = 45.
What if a equals b?
If a = b, then a² - b² = 0, and the factored form (a + b)(a - b) also equals 0 because (a - b) = 0.
工作原理
Calculates the difference between two squares and shows the factored form (a² - b² = (a + b)(a - b)).
- Enter the values for a and b.
- Square each value: a² and b².
- Subtract b² from a² to get the difference.
- The factored form is (a + b)(a - b), which equals the same result.
公式
此计算器背后的数学公式，供您核对结果。
Difference of Squares
This identity states that the difference between two squares equals the product of the sum and difference of the two numbers.
Example:
Input: a = 5, b = 3
Calculation: 5² - 3² = 25 - 9 = 16, and (5+3)(5-3) = 8 × 2 = 16
Result: 16
实际应用场景
此计算在日常生活中的应用。
Simplifying algebraic expressions
Factor expressions like x² - 9 quickly into (x + 3)(x - 3).
Example: x² - 9 = (x + 3)(x - 3)
Mental math
Compute differences of squares without a calculator, e.g., 99² - 1² = (99+1)(99-1) = 100 × 98 = 9800.
Example: 99² - 1² = 9800
Solving equations
Use the identity to solve quadratic equations that are in the form a² = b².
Example: x² = 16 → x² - 16 = 0 → (x+4)(x-4)=0 → x = ±4
提示与常见错误
Tips
- Remember the identity: a² - b² = (a + b)(a - b).
- Check your result by expanding (a + b)(a - b) to see if you get a² - b².
- The formula works for any real numbers, including fractions and decimals.
- Use the factored form to simplify calculations when a and b are large.
Common Mistakes to Avoid
- Forgetting that a² - b² is not equal to (a - b)². (a - b)² = a² - 2ab + b².
- Confusing the order: a² - b² is not the same as b² - a² unless you factor out a negative.
- When a and b are negative, forgetting that squaring makes them positive.
假设与限制
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.