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Difference of Squares Calculator.

Calculates the difference between two squares and shows the factored form (a² - b² = (a + b)(a - b)).

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Your inputs

How it works

  1. 1

    Enter the values for a and b.

  2. 2

    Square each value: a² and b².

  3. 3

    Subtract b² from a² to get the difference.

  4. 4

    The factored form is (a + b)(a - b), which equals the same result.

a^2 - b^2

Frequently asked questions

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.

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Difference of squares

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Factored form (a+b)(a-b)0
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How it works

Calculates the difference between two squares and shows the factored form (a² - b² = (a + b)(a - b)).

  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.

Formulas

The math behind this calculator, written out so you can verify the result.

Difference of Squares

a² - b² = (a + b)(a - b)

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

Real-world use cases

Where this calculation shows up in everyday life.

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

Tips and common mistakes

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.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.