Factor or expand algebraic expressions using the difference of two squares identity.
Operation Mode
Identity Variables
Visual Logic
x² - 25
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(x + 5)(x - 5)
Algebraic Result
(x + 5)(x - 5)
Factored Form
Opposite Form
x² - 25
Factoring breaks the difference into a sum and a difference of the square roots.
What is Difference of Squares?
The difference of two squares is an identity in algebra where an expression of the form a² - b² can be factored into (a + b)(a - b). This identity is widely used for simplifying expressions, solving quadratic equations, and mental math tricks.
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Pro Tips
Both terms must be perfect squares for this rule to apply easily.
The terms must be separated by a minus sign (difference).
You can use this to quickly multiply numbers like 19 × 21 by seeing it as (20-1)(20+1) = 20² - 1² = 399.
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Fun Facts
"In geometry, this represents the area remaining when a smaller square is removed from a larger one."
"This identity is a specific case of the more general 'Difference of nth Powers'."
"It is a fundamental tool used in the process of 'rationalizing the denominator' in calculus."
