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Algebra

Difference of Two Squares

Factor difference of two squares. Free online Difference of Two Squares. Calculate difference of two squares online — fast, accurate, mobile-friendly, no signup

a² − b² = (a+b)(a−b)
65

Derivation

  1. ├── 01Givena = 9, b = 4
  2. ├── 02Formulat²-a²
  3. ├── 03Substitutet²-9²
  4. └── 04Compute a² − b² = (a+b)(a−b)65
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§01What is

Understanding the Difference of Two Squares

The Difference of Two Squares computes a² − b² = (a+b)(a−b) from 2 inputs: a, b. Factor difference of two squares.

Algebra is the art of solving for the unknown. Rearranging a formula to isolate the variable you actually need is the single most common real-world math skill — and doing it with real numbers under time pressure is where errors happen. The Difference of Two Squares sits in that toolkit — it factor difference of two squares. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

t²-a²

Where

a
a
b
b
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: a = 9, b = 4.

  1. 01Start by noting the input — a: 9.
  2. 02Start by noting the input — b: 4.
  3. 03Substitute these values into the formula: t²-a²
  4. 04Compute a² − b² = (a+b)(a−b): the calculator returns 65.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Difference of Two Squares Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

a halved

a = 4.5 (from 9)

Keep every other input at its default and halve the a. See how a² − b² = (a+b)(a−b) responds.

  1. 01New a: 4.5
  2. 02Baseline a² − b² = (a+b)(a−b): 65
  3. 03New a² − b² = (a+b)(a−b): 4.25
  4. 04a² − b² = (a+b)(a−b) decreases by 93.5% → use this sensitivity to plan for real-world variation.
02 · PATTERN

a doubled

a = 18 (from 9)

Keep every other input at its default and double the a. See how a² − b² = (a+b)(a−b) responds.

  1. 01New a: 18
  2. 02Baseline a² − b² = (a+b)(a−b): 65
  3. 03New a² − b² = (a+b)(a−b): 308
  4. 04a² − b² = (a+b)(a−b) increases by 373.8% → use this sensitivity to plan for real-world variation.
03 · PATTERN

b halved

b = 2 (from 4)

Keep every other input at its default and halve the b. See how a² − b² = (a+b)(a−b) responds.

  1. 01New b: 2
  2. 02Baseline a² − b² = (a+b)(a−b): 65
  3. 03New a² − b² = (a+b)(a−b): 77
  4. 04a² − b² = (a+b)(a−b) increases by 18.5% → use this sensitivity to plan for real-world variation.
04 · PATTERN

b doubled

b = 8 (from 4)

Keep every other input at its default and double the b. See how a² − b² = (a+b)(a−b) responds.

  1. 01New b: 8
  2. 02Baseline a² − b² = (a+b)(a−b): 65
  3. 03New a² − b² = (a+b)(a−b): 17
  4. 04a² − b² = (a+b)(a−b) decreases by 73.8% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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