Can a sum of squares be factored?

Not over the real numbers: a² + b² only factors using complex numbers, (a + bi)(a − bi).

Difference of Squares

Factors the difference of two perfect squares.

a^{2} - b^{2} = (a - b) (a + b)

Variables

a, b: Any expressions

Explanation

Multiplying $(a - b) (a + b)$ gives $a^{2} + ab - ab - b^{2} = a^{2} - b^{2}$ ; the middle terms cancel. Recognizing this pattern makes factoring and simplifying rational expressions fast.

Example

$4 x^{2} - 25 = (2 x)^{2} - 5^{2} = (2 x - 5) (2 x + 5)$ .

Try it: Factoring Calculator

Factor polynomials completely: GCF, trinomials, difference of squares, sum of cubes and higher-degree polynomials.

Open calculator

Frequently asked questions

Related formulas

Sum and Difference of Cubes

Factors sums and differences of perfect cubes.