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Difference of Squares Calculator

Factor a² - b² into (a - b)(a + b)

a =b =

Difference of Squares Formula

a² - b² = (a - b)(a + b)

The difference of squares identity applies when two squared quantities are separated by subtraction. It factors the expression into conjugate binomials, one using a minus sign and the other using a plus sign. When the two binomials are multiplied back together, the middle terms cancel, leaving only a² and -b². This makes the identity useful for quick factoring and mental arithmetic.

⚠Note: This numeric version factors A²-B². Use symbolic A and B names conceptually in the formula.

What Is Difference of Squares?

A difference of squares is a subtraction expression where both terms are perfect squares. It factors into conjugate binomials, one with subtraction and one with addition.

Pattern

Both terms must be squares and there must be subtraction between them.

Conjugates

The factors are conjugates: (a-b) and (a+b).

Cancellation

The middle terms cancel when the conjugates are multiplied.

Check

Expand (a-b)(a+b) to verify a²-b².

💡 Example: 12²-5²=(12-5)(12+5)=7×17=119.

Applications

FactoringMental MathQuadratics

Frequently Asked Questions

What is a difference of squares calculator?▼

A difference of squares calculator factors expressions of the form a²-b² into (a-b)(a+b).

What is the difference of squares formula?▼

The formula is a²-b²=(a-b)(a+b).

Why does the middle term disappear?▼

When (a-b)(a+b) is expanded, +ab and -ab cancel each other.

Can x²-25 be factored this way?▼

Yes. x²-25 equals x²-5², so it factors as (x-5)(x+5).

Is a sum of squares factorable over real numbers?▼

A sum such as a²+b² does not factor over real numbers using this identity.

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