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Math

Verified calculator with a transparent formula

Math

Difference of Squares Calculator.

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

Results update live as you type.

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Your inputs

Value of a

Value of b

How it works

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

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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Results

Formula checked

Difference of squares

16

Factored form (a+b)(a-b)16.00

Estimate for general guidance only — verify important decisions with an appropriate professional.

How it works

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.

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.

MathifyCalculator tools

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此计算器目前以英文显示，翻译正在准备中。

数学

已验证计算器，公式透明

数学

Difference of Squares Calculator.

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

结果随输入实时更新。

ƒ

您的输入

Value of a

Value of b

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.

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结果

公式已检查

Difference of squares

16

Factored form (a+b)(a-b)16.00

询问任何问题

估算仅供参考——重要决策请咨询专业人士。

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

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

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.